ON THE CONSISTENCY OF TWISTED GENERALIZED WEYL ALGEBRAS
| Contribuinte(s) |
UNIVERSIDADE DE SÃO PAULO |
|---|---|
| Data(s) |
05/11/2013
05/11/2013
2012
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| Resumo |
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. FAPESP FAPESP [2008/10688-1, 2010/50347-9] CNPq CNPq [301743/2007-0] |
| Identificador |
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, PROVIDENCE, v. 140, n. 10, supl., Part 1-2, pp. 3349-3363, OCT, 2012 0002-9939 |
| Idioma(s) |
eng |
| Publicador |
AMER MATHEMATICAL SOC PROVIDENCE |
| Relação |
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY |
| Direitos |
openAccess Copyright AMER MATHEMATICAL SOC |
| Palavras-Chave | #SIMPLE WEIGHT MODULES #MATHEMATICS, APPLIED #MATHEMATICS |
| Tipo |
article original article publishedVersion |
