Noncommutative Rational Double Points

Abstract

In this paper we study noncommutative analogues of rational double points. The approach is to consider the action of a finite group G on certain noncommutative analogues of k[[x,y]] which were studied by Artin and Stafford (“Regular Local Rings of Dimension 2,” manuscript). An explicit description in terms of generators and relations is given for a large class of such algebras when G is cyclic. Finally, we show that these algebras are AS-Gorenstein of dimension two, have finite representation type and, in many cases, are regular in codimension one.