4
4.0
Jun 29, 2018
06/18
by
A-Ming Liu; Tongsuo Wu
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For each Boolean graph $B_n$, it is proved that both $B_n$ and its complement graph $\overline{B_n}$ are vertex decomposable. It is also proved that $B_n$ is an unmixed graph, thus it is also Cohen-Macaulay.
Topics: Commutative Algebra, Combinatorics, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1611.07574
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8.0
Jun 30, 2018
06/18
by
A. -H. Nokhodkar
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We associate to every central simple algebra with involution of orthogonal type in characteristic two a totally singular quadratic form which reflects certain anisotropy properties of the involution. It is shown that this quadratic form can be used to classify totally decomposable algebras with orthogonal involution. Also, using this form, a criterion is obtained for an orthogonal involution on a split algebra to be conjugated to the transpose involution.
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1701.02169
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17
Jun 26, 2018
06/18
by
A. Anastasiou; L. Borsten; M. J. Hughes; S. Nagy
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Tensoring two on-shell super Yang-Mills multiplets in dimensions $D\leq 10$ yields an on-shell supergravity multiplet, possibly with additional matter multiplets. Associating a (direct sum of) division algebra(s) $\mathbb{D}$ with each dimension $3\leq D\leq 10$ we obtain formulae for the algebras $\mathfrak{g}$ and $\mathfrak{h}$ of the U-duality group $G$ and its maximal compact subgroup $H$, respectively, in terms of the internal global symmetry algebras of each super Yang-Mills theory. We...
Topics: High Energy Physics - Theory, Mathematics, Representation Theory, Rings and Algebras
Source: http://arxiv.org/abs/1502.05359
5
5.0
Jun 30, 2018
06/18
by
A. B. Németh; S. Z. Németh
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While studying some properties of linear operators in a Euclidean Jordan algebra, Gowda, Sznajder and Tao have introduced generalized lattice operations based on the projection onto the cone of squares. In two recent papers of the authors of the present paper it has been shown that these lattice-like operators and their generalizations are important tools in establishing the isotonicity of the metric projection onto some closed convex sets. The results of this kind are motivated by metods for...
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1401.3581
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22
Jun 30, 2018
06/18
by
A. Calderón; C. Draper; C. Martín; T. Sánchez
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We describe the fine (group) gradings on the Heisenberg algebras, on the Heisenberg superalgebras and on the twisted Heisenberg algebras. We compute the Weyl groups of these gradings. Also the results obtained respect to Heisenberg superalgebras are applied to the study of Heisenberg Lie color algebras.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1405.4093
4
4.0
Jun 30, 2018
06/18
by
A. Dugas; B. Huisgen-Zimmermann
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For any truncated path algebra $\Lambda$, we give a structural description of the modules in the categories ${\cal P}^{
Topics: Mathematics, Rings and Algebras, Representation Theory
Source: http://arxiv.org/abs/1407.2690
3
3.0
Jun 30, 2018
06/18
by
A. Dugas; B. Huisgen-Zimmermann; J. Learned
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It is shown that path algebras modulo relations of the form $\Lambda = KQ/I$, where $Q$ is a quiver, $K$ a coefficient field, and $I \subseteq KQ$ the ideal generated by all paths of a given length, can be readily analyzed homologically, while displaying a wealth of phenomena. In particular, the syzygies of their modules, and hence their finitistic dimensions, allow for smooth descriptions in terms of $Q$ and the Loewy length of $\Lambda$. The same is true for the distributions of projective...
Topics: Mathematics, Rings and Algebras, Representation Theory
Source: http://arxiv.org/abs/1407.2672
3
3.0
Jun 30, 2018
06/18
by
A. G. Gorinov
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The fundamental theorem of affine geometry says that a self-bijection $f$ of a finite-dimensional affine space over a possibly skew field takes left affine subspaces to left affine subspaces of the same dimension, then $f$ of the expected type, namely $f$ is a composition of an affine map and an automorphism of the field. We prove a two-sided analogue of this: namely, we consider self-bijections as above which take affine subspaces affine subspaces but which are allowed to take left subspaces...
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1702.07701
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7.0
Jun 30, 2018
06/18
by
A. Ghorbani; S. K. Jain; Z. Nazemian
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Dimensions like Gelfand, Krull, Goldie have an intrinsic role in the study of theory of rings and modules. They provide useful technical tools for studying their structure. In this paper we define one of the dimensions called couniserial dimension that measures how close a ring or module is to being uniform. Despite their different objectives, it turns out that there are certain common properties between the couniserial dimension and Krull dimension like each module having such a dimension...
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1408.0056
3
3.0
Jun 29, 2018
06/18
by
A. Grishkov; J. M. Pérez-Izquierdo
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We develop Lie's correspondence and an explicit Baker-Campbell-Hausdorff formula for commutative automorphic formal loops.
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1612.03624
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19
Jun 27, 2018
06/18
by
A. H. Mokhtari; F. Moafian; H. R. Ebrahimi Vishki
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In this paper we provide some conditions under which a Lie derivation on a trivial extension algebra is proper, that is, it can be decomposed into the sum of a derivation and a center valued map. We extend some known results on the properness of Lie derivations of triangular algebras. Some illuminating examples are also included.
Topics: Rings and Algebras, Mathematics, Operator Algebras
Source: http://arxiv.org/abs/1504.05924
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58
Jun 27, 2018
06/18
by
A. H. Mokhtari; H. R. Ebrahimi Vishki
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Motivated by the Cheung's elaborate work [Linear Multilinear Algebra, 51 (2003), 299-310], we investigate the construction of a Lie derivation on a generalized matrix algebra and apply it to give a characterization for such a Lie derivation to be proper. Our approach not only provides a direct proof for some known results in the theory, but also it presents several sufficient conditions assuring the properness of Lie derivations on certain generalized matrix algebras.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1505.02344
5
5.0
Jun 30, 2018
06/18
by
A. J. Calderón; L. M. Camacho; B. A. Omirov
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We introduce and provide a classification theorem for the class of Heisenberg-Fock Leibniz algebras. This category of algebras is formed by those Leibniz algebras $L$ whose corresponding Lie algebras are Heisenberg algebras $H_n$ and whose ${H_n}$-modules $I$, where $I$ denotes the ideal generated by the squares of elements of $L$, are isomorphic to Fock modules. We also consider the three-dimensional Heisenberg algebra $H_3$ and study three classes of Leibniz algebras with $H_3$ as...
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1411.3861
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6.0
Jun 26, 2018
06/18
by
A. Kh. Khudoyberdiyev
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This paper is devoted to the description of complex finite-dimensional algebras of level two. We obtain the classification of algebras of level two in the varieties of Jordan, Lie and associative algebras.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1502.05813
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Jun 27, 2018
06/18
by
A. Kh. Khudoyberdiyev; M. Ladra; K. K. Masutova; B. A. Omirov
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In the present paper we indicate some Leibniz algebras whose closures of orbits under the natural action of $\GL_n$ form an irreducible component of the variety of complex $n$-dimensional Leibniz algebras. Moreover, for these algebras we calculate the bases of their second groups of cohomologies.
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1504.01216
7
7.0
Jun 29, 2018
06/18
by
A. L. Agore
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We completely describe by generators and relations and classify all Hopf algebras which factorize through the Taft algebra $T_{m^{2}}(q)$ and the group Hopf algebra $K[C_{n}]$: they are $nm^{2}$-dimensional quantum groups $T_{nm^{2}}^ {\omega}(q)$ associated to an $n$-th root of unity $\omega$. Furthermore, using Dirichlet's prime number theorem we are able to count the number of isomorphism types of such Hopf algebras. More precisely, if $d = {\rm gcd}(m,\,\nu(n))$ and...
Topics: Quantum Algebra, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1611.05674
5
5.0
Jun 30, 2018
06/18
by
A. L. Agore
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Using Wederburn's main theorem and a result of Gerstenhaber we prove that, over a field of characteristic zero, the maximal dimension of a proper unital subalgebra in the $n \times n$ matrix algebra is $n^2 - n + 1$ and furthermore this upper bound is attained for the so-called parabolic subalgebras. We also investigate the corresponding notion of parabolic coideals for matrix coalgebras and prove that the minimal dimension of a non-zero coideal of the matrix coalgebra ${\mathcal M}^n (k)$ is...
Topics: Mathematics, Quantum Algebra, Rings and Algebras
Source: http://arxiv.org/abs/1403.0773
5
5.0
Jun 30, 2018
06/18
by
A. L. Agore
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We construct the analogue of Takeuchi's free Hopf algebra in the setting of Poisson Hopf algebras. More precisely, we prove that there exists a free Poisson Hopf algebra on any coalgebra or, equivalently that the forgetful functor from the category of Poisson Hopf algebras to the category of coalgebras has a left adjoint. In particular, we also prove that the category of Poisson Hopf algebras is a reflective subcategory of the category of Poisson bialgebras. Along the way, we describe...
Topics: Quantum Algebra, Mathematics, Category Theory, Rings and Algebras
Source: http://arxiv.org/abs/1404.0170
6
6.0
Jun 30, 2018
06/18
by
A. L. Agore; G. Militaru
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We prove that the celebrated It\^{o}'s theorem for groups remains valid at the level of Leibniz algebras: if $\mathfrak{g}$ is a Leibniz algebra such that $\mathfrak{g} = A + B$, for two abelian subalgebras $A$ and $B$, then $\mathfrak{g}$ is metabelian, i.e. $[ \, [\mathfrak{g}, \, \mathfrak{g}], \, [ \mathfrak{g}, \, \mathfrak{g} ] \, ] = 0$. A structure type theorem for metabelian Leibniz/Lie algebras is proved. All metabelian Leibniz algebras having the derived algebra of dimension $1$ are...
Topics: Mathematics, Rings and Algebras, Differential Geometry
Source: http://arxiv.org/abs/1401.4675
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11
Jun 28, 2018
06/18
by
A. L. Agore; G. Militaru
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We introduce some basic concepts for Jacobi-Jordan algebras such as: representations, crossed products or Frobenius/metabelian/co-flag objects. A new family of solutions for the quantum Yang-Baxter equation is constructed arising from any $3$-step nilpotent Jacobi-Jordan algebra. Crossed products are used to construct the classifying object for the extension problem in its global form. For a given Jacobi-Jordan algebra $A$ and a given vector space $V$ of dimension $\mathfrak{c}$, a global...
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1507.08146
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12
Jun 27, 2018
06/18
by
A. L. Agore; G. Militaru
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Let $A$ be a unital associative algebra over a field $k$, $E$ a vector space and $\pi : E \to A$ a surjective linear map with $V = {\rm Ker} (\pi)$. All algebra structures on $E$ such that $\pi : E \to A$ becomes an algebra map are described and classified by an explicitly constructed global cohomological type object ${\mathbb G} {\mathbb H}^{2} \, (A, \, V)$. Any such algebra is isomorphic to a Hochschild product $A \star V$, an algebra introduced as a generalization of a classical...
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1503.05364
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14
Jun 27, 2018
06/18
by
A. L. Agore; G. Militaru
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If $\mathfrak{g} \subseteq \mathfrak{h}$ is an extension of Lie algebras over a field $k$ such that ${\rm dim}_k (\mathfrak{g}) = n$ and ${\rm dim}_k (\mathfrak{h}) = n + m$, then the Galois group ${\rm Gal} \, (\mathfrak{h}/\mathfrak{g})$ is explicitly described as a subgroup of the canonical semidirect product of groups ${\rm GL} (m, \, k) \rtimes {\rm M}_{n\times m} (k)$. An Artin type theorem for Lie algebras is proved: if a group $G$ whose order is invertible in $k$ acts as automorphisms...
Topics: Mathematical Physics, Mathematics, Rings and Algebras, Representation Theory
Source: http://arxiv.org/abs/1505.07346
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10.0
Jun 30, 2018
06/18
by
A. L. Agore; G. Militaru
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Jacobi/Poisson algebras are algebraic counterparts of Jacobi/Poisson manifolds. We introduce representations of a Jacobi algebra $A$ and Frobenius Jacobi algebras as symmetric objects in the category. A characterization theorem for Frobenius Jacobi algebras is given in terms of integrals on Jacobi algebras. For a vector space $V$ a non-abelian cohomological type object ${\mathcal J}{\mathcal H}^{2} \, (V, \, A)$ is constructed: it classifies all Jacobi algebras containing $A$ as a subalgebra of...
Topics: Mathematics, Rings and Algebras, Representation Theory, Differential Geometry
Source: http://arxiv.org/abs/1406.3529
4
4.0
Jun 30, 2018
06/18
by
A. Mani
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Rough sets over generalized transitive relations like proto-transitive ones had been initiated by the present author in the year 2012. Subsequently, approximation of proto-transitive relations by other relations was investigated and the relation with rough approximations was developed towards constructing semantics that can handle fragments of structure. It was also proved that difference of approximations induced by some approximate relations need not induce rough structures. In this research...
Topics: Mathematics, Logic, Computing Research Repository, Rings and Algebras, Artificial Intelligence
Source: http://arxiv.org/abs/1410.0572
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8.0
Jun 30, 2018
06/18
by
A. Melakhessou; K. Guenda; T. A. Gulliver; M. Shi; P. Solé
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In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring $R=\F_{q}+v\F_{q}+v^{2}\F_{q}$, where $v^{3}=v$, for $q$ odd. We give conditions on the existence of LCD codes and present construction of formally self-dual codes over $R$. Further, we give bounds on the minimum distance of LCD codes over $\F_q$ and extend these to codes over $R$.
Topics: Rings and Algebras, Information Theory, Computing Research Repository, Mathematics
Source: http://arxiv.org/abs/1704.03519
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7.0
Jun 30, 2018
06/18
by
A. N. Abyzov
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We describe rings over which every right module is almost injective. We give a description of rings over which every simple module is a almost projective.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1701.00026
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3.0
Jun 30, 2018
06/18
by
A. N. Abyzov; T. H. N. Nhan
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In this paper, we introduce and study the concept of CS-Rickart modules, that is a module analogue of the concept of ACS rings. A ring $R$ is called a right weakly semihereditary ring if every its finitly generated right ideal is of the form $P\oplus S,$ where $P_R$ is a projective module and $S_R$ is a singular module. We describe the ring $R$ over which $\mathrm{Mat}_n (R)$ is a right ACS ring for any $n \in \mathbb {N}$. We show that every finitely generated projective right $R$-module will...
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1406.3813
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5.0
Jun 29, 2018
06/18
by
A. N. Shevlyakov
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Equations over linearly ordered semilattices are studied. For any equation $t(X)=s(X)$ we find irreducible components of its solution set and compute the average number of irreducible components of all equations in $n$ variables.
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1601.03875
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4.0
Jun 30, 2018
06/18
by
A. Nyman
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Let $k$ be a field. We describe necessary and sufficient conditions for a $k$-linear abelian category to be a noncommutative $\mathbb{P}^{1}$-bundle over a pair of division rings over $k$. As an application, we prove that $\mathbb{P}^{1}_{n}$, Piontkovski's $n$th noncommutative projective line, is the noncommutative projectivization of an $n$-dimensional vector space.
Topics: Quantum Algebra, Rings and Algebras, Algebraic Geometry, Mathematics
Source: http://arxiv.org/abs/1704.04544
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5.0
Jun 29, 2018
06/18
by
A. O. Abdulkareem; M. A. Fiidow; I. S. Rakhimov
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In this paper, we focus on derivations and centroids of four dimensional associative algebras. Using an existing classification result of low dimensional associative algebras, we describe the derivations and centroids of four dimensional associative algebras. We also identify algebra(s) that belong to the characteristically nilpotent class among the algebras of four dimensional associative algebras.
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1606.03119
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7.0
Jun 28, 2018
06/18
by
A. P. Kitchin; S. Launois
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Motivated by Weyl algebra analogues of the Jacobian conjecture and the Tame Generators problem, we prove quantum versions of these problems for a family of analogues to the Weyl algebras. In particular, our results cover the Weyl-Hayashi algebras and tensor powers of a quantization of the first Weyl algebra which arises as a primitive factor algebra of $U_q^+(\mathfrak{so}_5)$.
Topics: Rings and Algebras, Quantum Algebra, Mathematics
Source: http://arxiv.org/abs/1511.01775
4
4.0
Jun 29, 2018
06/18
by
A. P. Petravchuk
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Let $K$ be an arbitrary field of characteristic zero and $A$ a commutative associative $ K$-algebra which is an integral domain. Denote by $R$ the fraction field of $A$ and by $W(A)=RDer_{\mathbb K}A,$ the Lie algebra of $\mathbb K$-derivations of $R$ obtained from $Der_{\mathbb K}A$ via multiplication by elements of $R.$ If $L\subseteq W(A)$ is a subalgebra of $W(A)$ denote by $rk_{R}L$ the dimension of the vector space $RL$ over the field $R$ and by $F=R^{L}$ the field of constants of $L$ in...
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1601.04313
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3.0
Jun 30, 2018
06/18
by
A. P. Petravchuk; K. Ya. Sysak
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Let $\mathbb K$ be an algebraically closed field of characteristic zero. Let $V$ be a module over the polynomial ring $\mathbb K[x,y]$. The actions of $x$ and $y$ determine linear operators $P$ and $Q$ on $V$ as a vector space over $\mathbb K$. Define the Lie algebra $L_V=\mathbb K\langle P,Q\rangle \rightthreetimes V$ as the semidirect product of two abelian Lie algebras with the natural action of $\mathbb K\langle P,Q\rangle$ on $V$. We show that if $\mathbb K[x,y]$-modules $V$ and $W$ are...
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1701.03750
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5.0
Jun 29, 2018
06/18
by
A. P. Petravchuk; K. Ya. Sysak
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Let $K$ be an algebraically closed field of characteristic zero and $A$ an integral $K$-domain. The Lie algebra $Der_{K}(A)$ of all $K$-derivations of $A$ contains the set $LND(A)$ of all locally nilpotent derivations. The structure of $LND(A)$ is of great interest, and the question about properties of Lie algebras contained in $LND(A)$ is still open. An answer to it in the finite dimensional case is given. It is proved that any finite dimensional (over $K$) subalgebra of $Der_{K}(A)$...
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1608.01490
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6.0
Jun 28, 2018
06/18
by
A. Pakharev; M. Skopenkov
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We find all analytic surfaces in space R^3 such that through each point of the surface one can draw two circular arcs fully contained in the surface. The proof uses a new decomposition technique for quaternionic matrices.
Topics: Rings and Algebras, Algebraic Geometry, Mathematics
Source: http://arxiv.org/abs/1510.06510
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12
Jun 28, 2018
06/18
by
A. R. Rajan; Azeef Muhammed P A
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Let $T_X$ be the semigroup of all non-invertible transformations on an arbitrary set $X$. It is known that $T_X$ is a regular semigroup. The principal right(left) ideals of a regular semigroup $S$ with partial left(right) translations as morphisms form a normal category $\mathcal{R}( S )$($\mathcal{L}( S )$). Here we consider the category $\Pi(X)$ of partitions of a set $X$ and show that it admits a normal category structure and that $\Pi(X)$ is isomorphic to the category $\mathcal{R}( T_X )$....
Topics: Group Theory, Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1509.02888
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7.0
Jun 29, 2018
06/18
by
A. Rezaei-Aghdam; L. Sedghi-Ghadim
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In this paper by use of cohomology complex of $3$-Leibniz algebras, the definitions of Leibniz bialgebras (and Lie bialgebras) are extended for the case of $3$-Leibniz algebras. Many theorems about Leibniz bialgebras are extended and proved for the case of $3$-Leibniz bialgebras ($3$-Lie bialgebras). Moreover a new theorem on the correspondence between $3$-Leibniz bialgebra and its associated Leibniz bialgebra is proved. $3$-Lie bialgebra as particular case of the $3$-Leibniz bialgebra is...
Topics: Mathematical Physics, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1604.04475
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4.0
Jun 29, 2018
06/18
by
A. S. Dzhumadil'daev
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We prove that assosymmetric algebras under Jordan product are Lie triple. A Lie triple algebra is called special if it is isomorphic to a subalgebra of some plus-assosymmetric algebra. We establish that Glennie identitiy is valid for special Lie triple algebras, but not for all Lie triple algebras.
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1601.06238
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17
Jun 29, 2018
06/18
by
A. S. Dzhumadil'daev
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We give presentation of composition inverse of formal power serie in a logarithmic form.
Topics: Combinatorics, Classical Analysis and ODEs, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1602.03728
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10.0
Jun 28, 2018
06/18
by
A. S. Hegazi; Hani Abdelwahab
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The paper is devoted to the study of annihilator extensions of evolution algebras and suggests an approach to classify finite-dimensional nilpotent evolution algebras. Subsequently nilpotent evolution algebras of dimension up to four are classfied.
Topics: Commutative Algebra, Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1508.06860
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17
Jun 28, 2018
06/18
by
A. S. Hegazi; Hani Abdelwahab
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The paper is devoted to give a complete classification of five-dimension nilpotent evolution algebras over an algebraically closed field. We obtained a list of 27 isolated non-isomorphic nilpotent evolution algebras and 2 families of non-isomorphic algebras depending on one parameter.
Topics: Commutative Algebra, Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1508.07442
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8.0
Jun 30, 2018
06/18
by
A. S. Hegazi; Hani Abdelwahab
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The paper is devoted to classify nilpotent Jordan algebras of dimension up to five over an algebraically closed field of characteristic not 2. We obtained a list of 35 isolated non-isomorphic 5-dimensional nilpotent non-associative Jordan algebras and 6 families of non-isomorphic 5-dimensional nilpotent non-associative Jordan algebras depending either on one or two parameters over an algebraically closed field of characteristic not 2 or 3. In addition to these algebras we obtained two...
Topics: Mathematics, Rings and Algebras, Mathematical Physics, Commutative Algebra
Source: http://arxiv.org/abs/1401.3992
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9.0
Jun 29, 2018
06/18
by
A. Salch
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It is well-known that the category of comodules over a flat Hopf algebroid is abelian but typically fails to have enough projectives, and more generally, the category of graded comodules over a graded flat Hopf algebroid is abelian but typically fails to have enough projectives. In this short paper we prove that the category of connective graded comodules over a connective, graded, flat, finite-type Hopf algebroid has enough projectives. Applications in algebraic topology are given: the Hopf...
Topics: Algebraic Topology, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1607.00749
3
3.0
Jun 29, 2018
06/18
by
A. Soman
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Let $F$ be a Henselian field of $q$-cohomological dimension $3$, where $q$ is a prime and let $\Gamma_F$ be the totally ordered abelian value group of $F$. Let $D$ be a central division algebra over $F$ of $q$-primary index such that the characteristic of the residue field $\overline{F}$, $char(\overline{F})$ is coprime to $q$. We show that when $cd_q(\overline{F})
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1609.01403
3
3.0
Jun 30, 2018
06/18
by
A. Stavrova
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Let k be a field of characteristic 0. Let G be a reductive group over the ring of Laurent polynomials R=k[x_1^{\pm 1},...,x_n^{\pm 1}] containing a maximal R-torus T (equivalently, loop reductive). Assume also that every semisimple normal subgroup of G contains a two-dimensional split torus G_m^2. We show that the natural map of non-stable K_1-functors K_1^G(R)-> K_1^G(k((x_1))...((x_n))) is injective. This complements the surjectivity result for the same map obtained by V. Chernousov, P....
Topics: Mathematics, Rings and Algebras, K-Theory and Homology, Group Theory
Source: http://arxiv.org/abs/1404.7587
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Jun 28, 2018
06/18
by
A. Tsurkov
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In this paper we consider the very wide class of varieties of representations of Lie algebras over the field k, which has characteristic 0. We study the relation between the geometric equivalence and automorphic equivalence of the representations of these varieties. We calculate the group, which measures the difference between the geometric equivalence and automorphic equivalence of representations of theses varieties. In Section 5, we present one example of the subvariety of the variety of all...
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1508.03034
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3.0
Jun 30, 2018
06/18
by
A. V. Bratchikov
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We construct a family of subalgebras of the Gerstenhaber algebra of differential operators. The subalgebras are labeled by subsets of the additive group ${\mathbb Z}^n$ that are closed under addition. Each subalgebra is invariant under the Hochschild coboundary operator.
Topics: Mathematics, Rings and Algebras, Mathematical Physics
Source: http://arxiv.org/abs/1411.4968
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3.0
Jun 29, 2018
06/18
by
A. V. Shepler; S. Witherspoon
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We build resolutions for general twisted tensor products of algebras. These bimodule and module resolutions unify many constructions in the literature and are suitable for computing Hochschild (co)homology and more generally Ext and Tor for (bi)modules. We analyze in detail the case of Ore extensions, consequently obtaining Chevalley-Eilenberg resolutions for universal enveloping algebras of Lie algebras (defining the cohomology of Lie groups and Lie algebras). Other examples include semidirect...
Topics: Representation Theory, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1610.00583
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9.0
Jun 30, 2018
06/18
by
A. V. Shvetsova; T. V. Skoraya
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The paper is devoted to two new results concerning varieties of Leibnitz algebras over a field of the zero characteristic. Here is proved the sufficient condition for finiteness colength of variety of Leibnitz algebras. Here is also defined the basis of identities of variety V3 of Leibnitz algebras and the basis of its multilinear part.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1405.4603
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4.0
Jun 30, 2018
06/18
by
A. Ya. Belov; A. L. Chernyatiev
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We investigate normal basis of algebras with small growth. The paper was supported by the Grant RFBR N 14-01-00548.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1412.7754
