3
3.0

Jan 18, 2022
01/22

by
James Zhang (James_Z)

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Ultimaker2的十字架结构调整。当十字架结构的X/Y相互不垂直，会造成十字架磨损，甚至打印失败，影像精度。 通过这个十字架调整工具，松开皮带齿轮顶丝，将工具卡到丝杆上，可以用于校正十字结构的相互垂直性。

Topics: stl, thingiverse, 3D Printer Parts

43
43

Sep 22, 2013
09/13

by
Kenneth Chan; Chelsea Walton; James Zhang

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Let H be a Hopf algebra with antipode S, and let A be an N-Koszul Artin-Schelter regular algebra. We study connections between the Nakayama automorphism of A and S^2 of H when H coacts on A inner-faithfully. Several applications pertaining to Hopf actions on Artin-Schelter regular algebras are given.

Source: http://arxiv.org/abs/1210.6432v1

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14

Jun 27, 2018
06/18

by
Kenneth Chan; Alexander Young; James Zhang

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We solve two conjectures of Ceken-Palmieri-Wang-Zhang concerning discriminants and give some applications.

Topics: Rings and Algebras, Mathematics, Quantum Algebra

Source: http://arxiv.org/abs/1503.06327

4
4.0

Jun 29, 2018
06/18

by
Kenneth Chan; Alexander Young; James Zhang

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We study important invariants and properties of the Veronese subalgebras of $q$-skew polynomial rings, including their discriminant, center and automorphism group, as well as cancellation property and the Tits alternative.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1606.01296

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109

Jun 29, 2018
06/18

by
Kenneth Chan; Ellen Kirkman; Chelsea Walton; James Zhang

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In establishing a more general version of the McKay correspondence, we prove Auslander's theorem for actions of semisimple Hopf algebras H on noncommutative Artin-Schelter regular algebras A of global dimension two, where A is a graded H-module algebra, and the Hopf action on A is inner faithful with trivial homological determinant. We also show that each fixed ring A^H under such an action arises an analogue of a coordinate ring of a Kleinian singularity.

Topics: Quantum Algebra, Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1607.06977

3
3.0

Jun 29, 2018
06/18

by
Kenneth Chan; Ellen Kirkman; Chelsea Walton; James Zhang

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We continue our study of the McKay Correspondence for grading preserving actions of semisimple Hopf algebras H on (noncommutative) Artin-Schelter regular algebras A. Here, we establish correspondences between module categories over A^H, over A\#H, and over \End_{A^H} A. We also study homological properties of (endomorphism rings of) maximal Cohen-Macaulay modules over A^H.

Topics: Quantum Algebra, Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1610.01220

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39

Sep 23, 2013
09/13

by
Kenneth Chan; Ellen Kirkman; Chelsea Walton; James Zhang

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We classify quantum analogues of actions of finite subgroups G of SL_2(k) on commutative polynomial rings k[u,v]. More precisely, we produce a classification of pairs (H,R), where H is a finite dimensional Hopf algebra that acts inner faithfully and preserves the grading of an Artin-Schelter regular algebra R of global dimension two. Remarkably, the corresponding invariant rings R^H share similar regularity and Gorenstein properties as the invariant rings k[u,v]^G in the classic setting. We...

Source: http://arxiv.org/abs/1303.7203v1

49
49

Sep 18, 2013
09/13

by
Kenneth Chan; Chelsea Walton; Yanhua Wang; James Zhang

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We study finite dimensional Hopf algebra actions on so-called filtered Artin-Schelter regular algebras of dimension n, particularly on those of dimension 2. The first Weyl algebra is an example of such on algebra with n=2, for instance. Results on the Gorenstein condition and on the global dimension of the corresponding fixed subrings are also provided.

Source: http://arxiv.org/abs/1211.6513v2

3
3.0

Jun 30, 2018
06/18

by
Secil Ceken; John Palmieri; Yanhua Wang; James Zhang

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We use the discriminant to determine the automorphism groups of some noncommutative algebras, and we prove that a family of noncommutative algebras has tractable automorphism groups.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1401.0793

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11

Jun 26, 2018
06/18

by
Secil Ceken; John H. Palmieri; Yanhua Wang; James Zhang

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We study the invariant theory of a class of quantum Weyl algebras under group actions and prove that the fixed subrings are always Gorenstein. We also verify the Tits alternative for the automorphism groups of these quantum Weyl algebras.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1501.07881

9
9.0

Jun 30, 2018
06/18

by
Secil Ceken; John H. Palmieri; Yanhua Wang; James Zhang

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We compute the automorphism groups of some quantized algebras, including tensor products of quantum Weyl algebras and some skew polynomial rings.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1402.6625