Ellen Kirkman, Wake Forest University
"The Invariant Theory of Artin-Schelter Regular Algebras"
Classical invariant theory studies the ring of invariants $\Bbbk[x_1, \dots, x_n]^G$ under the action of a group $G$ on a commutative polynomial ring $\Bbbk[x_1, \dots, x_n]$. To extend this theory to a noncommutative context, we replace the polynomial ring with an Artin-Schelter regular algebra $A$ (that when commutative is isomorphic to a commutative polynomial ring), and study the invariants $A^G$ under the action of a finite group, or, more generally, a semisimple Hopf algebra. In this talk we will present some results that generalize classical results in two cases: (1) the case when $G$ is a reflection group, and (2) the case when $G$ is a finite subgroup of SL$_n(\mathbb{C})$.
MC 5501