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• W2963133879 startingPage "8613" @default.
• W2963133879 abstract "In the 1960s Maurice Auslander proved the following important result. Let $R$ be the commutative polynomial ring $mathbb {C}[x_1,dots ,x_n]$, and let $G$ be a finite small subgroup of $textrm {GL}_n(mathbb {C})$ acting on $R$ naturally. Let $A$ be the fixed subring $R^G:={ain R|g(a)=a text { for all } gin G }$. Then the endomorphism ring of the right $A$-module $R_A$ is naturally isomorphic to the skew group algebra $Rast G$. In this paper, a version of the Auslander theorem is proven for the following classes of noncommutative algebras: (a) noetherian PI local (or connected graded) algebras of finite injective dimension, (b) universal enveloping algebras of finite-dimensional Lie algebras, and (c) noetherian graded down-up algebras." @default.
• W2963133879 created "2019-07-30" @default.
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• W2963133879 date "2018-06-26" @default.
• W2963133879 modified "2023-10-14" @default.
• W2963133879 title "Noncommutative Auslander theorem" @default.
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• W2963133879 doi "https://doi.org/10.1090/tran/7332" @default.
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