二维阿尔丁-谢尔特正则代数上的群协整

Pub Date : 2024-03-29 DOI:10.1090/proc/16844

Simon Crawford

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引用次数: 0

摘要

我们描述了二维阿尔丁-谢尔特正则代数上有限群的所有可能的协作用（等同于所有群分级）。我们给出了相关的奥斯兰德映射为同构的必要条件和充分条件，并精确地确定了共作用的不变环是阿尔丁-谢尔特正则的情况。我们对结果的证明是组合式的，并利用了与协作用相关的麦凯四维结构。

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Group coactions on two-dimensional Artin-Schelter regular algebras

We describe all possible coactions of finite groups (equivalently, all group gradings) on two-dimensional Artin-Schelter regular algebras. We give necessary and sufficient conditions for the associated Auslander map to be an isomorphism, and determine precisely when the invariant ring for the coaction is Artin-Schelter regular. The proofs of our results are combinatorial and exploit the structure of the McKay quiver associated to the coaction.

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