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- W5293057 abstract "Skew group algebras appear in connection with the studyof singularities [1], [2]. It was proved in [4], [6], [10] the preprojective algebra of an Euclidean diagram is Morita equivalent to a skew group algebra of a polynomial algebra. In [7] we investigated the Yoneda algebraof a selfinjective Koszul algebra and proved they have properties analogous to the commutative regular algebras, we call such algebras generalized Auslander regular. The aim of the paper is to prove that given a positively graded locally finite K-algebra Λ = ∑ί≥0Λί and a finite grading preserving group G of automorphisms of Λ, with characteristic K not dividing the order of G, then G acts naturally on the Yoneda algebra Γ =⊕κ≥0 ExtkΛ(Λ0,Λ0) and the skew group algebra Γ*G is isomorphicto the Yoneda algebra Λ*G = ⊕κ≥0 ExtκΛ*G(Λ0*G,Λ0*G). As an application we prove Λ is generalized Auslander regular if and only if Λ*G is generalized Auslander regular and Λ is Koszul if and only ifΛ*G is so." @default.
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- W5293057 date "2001-01-01" @default.
- W5293057 modified "2023-10-16" @default.
- W5293057 title "Skew Group Algebras and their Yoneda Algebras" @default.
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