Invariant theory of Artin-Schelter regular algebras: a survey

摘要

This is survey of results that extend notions of the classical invariant theory of linear actions by finite groups on k[x 1,..., x_n] to the setting of finite group or Hopf algebra H actions on an Artin-Schelter regular algebra A. We investigate when A~H is AS regular, or AS Gorenstein, or a "complete intersection" in a sense that is defined. Directions of related research are explored briefly.