Seminar

Let $k$ be an algebraically closed field of characteristic zero, $A$  be an Artin-Schelter regular algebra, and $G$ be a group of graded automorphisms of $A$.  J{\o}rgensen and Zhang proved that if all elements of $G$ have homological determinant 1, then $A^G$ is Artin-Schelter Gorenstein.  For a family of AS regular algebras of dimension 3 (the Noetherian graded down-up algebras) we determine when $A^G$ is a ``complete intersection" (in a sense to be defined), and we relate this condition to the form of the Hilbert series of $A^G$, and to generators of $G$.  For this class of algebras, we obtain an extension to $A$ of a theorem for $k[x_1, \cdots, x_n]$ due to Kac-Watanabe and Gordeev.

(This is joint work with James Kuzmanovich and James Zhang).