| Full text | |
| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] Univ Sao Paulo, Inst Matemat & Estat, BR-05315970 Sao Paulo - Brazil
[2] Stanford Univ, Dept Math, Stanford, CA 94305 - USA
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | Proceedings of the American Mathematical Society; v. 140, n. 10, p. 3349-3363, OCT 2012. |
| Web of Science Citations: | 4 |
| Abstract | |
A twisted generalized Weyl algebra A of degree n depends on a. base algebra R, n commuting automorphisms sigma(i) of R, n central elements t(i) of R and on some additional scalar parameters. In a paper by Mazorchuk and Turowska, it is claimed that certain consistency conditions for sigma(i) and t(i) are sufficient for the algebra to be nontrivial. However, in this paper we give all example which shows that this is false. We also correct the statement by finding a new set of consistency conditions and prove that the old and new conditions together are necessary and sufficient for the base algebra R to map injectively into A. In particular they are sufficient for the algebra A to be nontrivial. We speculate that these consistency relations may play a role in other areas of mathematics, analogous to the role played by the Yang-Baxter equation in the theory of integrable systems. (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 |