Abstract

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Let $G$ be a finite group acting on an Artin-Schelter regular $\mathbb{C}$-algebra 

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$A$. Extending results of Watanabe we give conditions when the invariant subring 

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$A^G$ is an Artin-Schelter Gorenstein algebra. When $A= \mathbb{C}[x_1, \cdots, x_n]$

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Gordeev (1986) and Nakajima (1984) independently determined when $A^G$ is a complete 

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intersection. We discuss extending these results to other Artin-Schelter regular algebras.

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This is joint work with J. Kuzmanovich and J.J. Zhang.