Gorenstein subrings of invariants under Hopf algebra actions
Gorenstein subrings of invariants under Hopf algebra actions
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DOI：
10.1016/j.jalgebra.2009.08.018
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发表时间：
2009-11
影响因子：
0.9
通讯作者：
E. Kirkman;J. Kuzmanovich;J. J. Zhang-J.
中科院分区：
文献类型：
--
作者：
E. Kirkman;J. Kuzmanovich;J. J. Zhang-J.
本文研究了有限维半单Hopf代数在Artin-Schelter正则代数上的作用，使得不变量的子环满足Artin-Schelter Gorenstein条件.经典的结果，如渡边定理和斯坦利定理的情况下，从一个群作用的范围内的一个霍普夫代数行动。引入了同调行列式的一个Hopf代数形式，它成为从群作用推广到Hopf代数作用的重要工具.
This paper concerns conditions on the action of a finite dimensional semisimple Hopf algebra on an Artin–Schelter regular algebra that force the subring of invariants to satisfy the Artin–Schelter Gorenstein condition. Classical results such as Watanabe's Theorem and Stanley's Theorem are extended from the case of a group action to the context of a Hopf algebra action. A Hopf algebra version of the homological determinant is introduced, and it becomes an important tool in the generalization from group actions to Hopf algebra actions.