# Mathematical Sciences Research Institute

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# Invariants of actions on Artin-Schelter regular algebras

## Connections for Women: Quantum Symmetries January 23, 2020 - January 24, 2020

January 23, 2020 (11:00 AM PST - 12:00 PM PST)
Speaker(s): Ellen Kirkman (Wake Forest University)
Location: MSRI: Simons Auditorium
Tags/Keywords
• Rings of invariants

• reflection Hopf algebra

• Noether bound

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
Video

#### 2-Kirkman

Abstract

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 finite dimensional Hopf algebra. We will discuss some open questions on generalizing classical results to this context.

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