Skew group algebras, invariants and Weyl Algebras

2012/11/05 by Martinez-Villa, Roberto, Mondragon, Jeronimo
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1211.0981

Abstract

The aim of this paper is two fold: First to study finite groups G of automorphisms of the homogenized Weyl algebra B_n, the skew group algebra B_n∗ G, the ring of invariants B_n^G, and the relations of these algebras with the Weyl algebra A_n, with the skew group algebra A_n∗ G, and with the ring of invariants A_n^G. Of particular interest is the case n=1. In the on the other hand, we consider the invariant ring \QTRslC[X]^G of the polynomial ring K[X] in n generators, where G is a finite subgroup of Gl(n,\QTRslC) such that any element in G different from the identity does not have one as an eigenvalue. We study the relations between the category of finitely generated modules over \QTRslC[X]^G and the corresponding category over the skew group algebra \QTRslC% [X]∗ G. We obtain a generalization of known results for n=2 and G a finite subgroup of Sl(2,C). In the last part of the paper we extend the results for the polynomial algebra C[X] to the homogenized Weyl algebra B_n.

Related

• Skew Hecke Algebras
• Invariants of (-1)-Skew Polynomial Rings under Permutation Representations
• Algebra structure on the Hochschild cohomology of the ring of invariants of a Weyl algebra under a finite group
• Skew derivations on generalized Weyl algebras
• Invariants of finite groups acting on (free) skew fields