Galois orders, twisted generalized Weyl algebras and their representations
Characters and cohomology of modules for affine Kac-Moody algebras and generalizat...
The Lie algebra of derivations on a polynomial ring and certain maximal subalgebras
| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Stanford Univ, Dept Math, Stanford, CA 94305 - USA
[2] Univ Copenhagen, Dept Math Sci, DK-2100 Copenhagen O - Denmark
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Journal of Algebra; v. 373, p. 312-339, JAN 1 2013. |
| Web of Science Citations: | 4 |
| Abstract | |
In this paper we prove three theorems about twisted generalized Weyl algebras (TGWAs). First, we show that each non-zero ideal of a TGWA has non-zero intersection with the centralizer of the distinguished subalgebra R. This is analogous to earlier result's known to hold for crystalline graded rings. Second, we give necessary and sufficient conditions for the centralizer of R to be commutative (hence maximal commutative), generalizing a result by V. Mazorchuk and L Turowska. And third, we generalize results by D.A. Jordan and V. Bavula on generalized Weyl algebras by giving necessary and sufficient conditions for certain TGWAs to be simple, in the case when R is commutative. We illustrate our theorems by considering some special classes of TGWAs and providing concrete examples. We also discuss how simplicity of a TGWA is related to the maximal commutativity of R and the (non-)existence of non-trivial Z(n)-invariant ideals of R. (C) 2012 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 08/10688-1 - Galois orders, twisted generalized Weyl algebras and their representations |
| Grantee: | Jonas Torbjorn Hartwig |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |