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Group coactions on two-dimensional Artin-Schelter regular algebras (2304.05937v1)
Published 12 Apr 2023 in math.RA and math.RT
Abstract: 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.