AUSLANDER'S THEOREM FOR PERMUTATION ACTIONS ON NONCOMMUTATIVE ALGEBRAS

被引：13

作者：

Gaddis, Jason ^{[1
]}

Kirkman, Ellen ^{[2
]}

Moore, W. Frank ^{[2
]}

Won, Robert ^{[3
]}

机构：

[1] Miami Univ, Dept Math, 301 S Patterson Ave, Oxford, OH 45056 USA

[2] Wake Forest Univ, Dept Math & Stat, POB 7388, Winston Salem, NC 27109 USA

[3] Univ Washington, Dept Math, Box 354350, Seattle, WA 98195 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 147卷 / 05期

基金：

芬兰科学院;

关键词：

SEMISIMPLE HOPF ACTIONS; MODULES;

D O I：

10.1090/proc/14363

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

When A = k[x(1),..., x(n)] and G is a small subgroup of GL(n)(k), Auslander's Theorem says that the skew group algebra A#G is isomorphic to End (G)(A)(A) as graded algebras. We prove a generalization of Auslander's Theorem for permutation actions on (-1)-skew polynomial rings, (-1)-quantum Weyl algebras, three-dimensional Sklyanin algebras, and a certain homogeneous down-up algebra. We also show that certain fixed rings A(G) are graded isolated singularities in the sense of Ueyama.

引用

页码：1881 / 1896

页数：16

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