Invariant Theory of Finite Group Actions on Down-Up Algebras
E. Kirkman, J. Kuzmanovich, and J.J. Zhang
TL;DR
This paper investigates the structure of fixed subrings under finite group actions on certain noncommutative algebras, extending classical invariant theory results to a noncommutative setting.
Contribution
It establishes a noncommutative analogue of the Kac-Watanabe and Gordeev theorem for Artin-Schelter regular algebras of dimension 2 and 3.
Findings
Fixed subrings are Artin-Schelter Gorenstein under certain conditions
Extension of classical invariant theory to noncommutative algebras
New criteria for Gorenstein properties of fixed subrings
Abstract
We study Artin-Schelter Gorenstein fixed subrings of some Artin-Schelter regular algebras of dimension 2 and 3 under finite group actions, and prove a noncommutative version of the Kac-Watanabe and Gordeev theorem for these algebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Operator Algebra Research · Advanced Topics in Algebra