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Invariant theory of finite group actions on down-up algebras. (English) Zbl 1356.16021

Summary: We study Artin-Schelter Gorenstein fixed subrings of some Artin-Schelter regular algebras of dimension 2 and 3 under a finite group action and prove a noncommutative version of the Kac-Watanabe and Gordeev theorem for these algebras.

MSC:

16S38 Rings arising from noncommutative algebraic geometry
16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
16W22 Actions of groups and semigroups; invariant theory (associative rings and algebras)
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