2 research outputs found
Skew group algebras, invariants and Weyl Algebras
The aim of this paper is two fold:
First to study finite groups of automorphisms of the homogenized Weyl
algebra , the skew group algebra , the ring of invariants
, and the relations of these algebras with the Weyl algebra ,
with the skew group algebra , and with the ring of invariants
. Of particular interest is the case .
In the on the other hand, we consider the invariant ring \QTR{sl}{C}[X]^{G}
of the polynomial ring in generators, where is a finite subgroup
of Gl(n,\QTR{sl}{C}) such that any element in different from the identity
does not have one as an eigenvalue. We study the relations between the category
of finitely generated modules over \QTR{sl}{C}[X]^{G} and the corresponding
category over the skew group algebra \QTR{sl}{C}% [X]\ast G. We obtain a
generalization of known results for and a finite subgroup of
. In the last part of the paper we extend the results for the
polynomial algebra to the homogenized Weyl algebra