Generalized Weyl algebras: category O and graded Morita equivalence
Abstract
We study the structural and homological properties of graded Artinian modules over generalized Weyl algebras (GWAs), and this leads to a decomposition result for the category of graded Artinian modules. Then we define and examine a category of graded modules analogous to the BGG category O. We discover a condition on the data defining the GWA that ensures O has a system of projective generators. Under this condition, O has nice representation-theoretic properties. There is also a decomposition result for O. Next, we give a necessary condition for there to be a strongly graded Morita equivalence between two GWAs. We define a new algebra related to GWAs, and use it to produce some strongly graded Morita equivalences. Finally, we give a complete answer to the strongly graded Morita problem for classical GWAs.
Keywords
Cite
@article{arxiv.0904.3743,
title = {Generalized Weyl algebras: category O and graded Morita equivalence},
author = {Ian Shipman},
journal= {arXiv preprint arXiv:0904.3743},
year = {2010}
}
Comments
19 pages