Generalized Weyl algebras: Category O and graded Morita equivalence

JOURNAL OF ALGEBRA

卷:323

Article

Shipman, Ian

关键词: Generalized Weyl algebras;    Morita equivalence;    Module categories;    Deformations of Kleinian singularities;   

DOI  :  10.1016/j.jalgebra.2010.02.027

来源: Elsevier

【 摘 要 】

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. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free