On the consistency of twisted generalized Weyl algebras
Authors:
Vyacheslav Futorny and Jonas T. Hartwig
Journal:
Proc. Amer. Math. Soc. 140 (2012), 33493363
MSC (2010):
Primary 16D30, 16S35; Secondary 16S85
Published electronically:
February 17, 2012
MathSciNet review:
2929005
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Abstract: A twisted generalized Weyl algebra of degree depends on a base algebra , commuting automorphisms of , central elements of and on some additional scalar parameters. In a paper by Mazorchuk and Turowska, it is claimed that certain consistency conditions for and are sufficient for the algebra to be nontrivial. However, in this paper we give an 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 to map injectively into . In particular they are sufficient for the algebra 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 YangBaxter equation in the theory of integrable systems.
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Additional Information
Vyacheslav Futorny
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo SP, 05315970, Brazil
Email:
futorny@ime.usp.br
Jonas T. Hartwig
Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305
Email:
jonas.hartwig@gmail.com
DOI:
http://dx.doi.org/10.1090/S000299392012111840
Received by editor(s):
March 22, 2011
Received by editor(s) in revised form:
April 7, 2011
Published electronically:
February 17, 2012
Communicated by:
Kailash C. Misra
Article copyright:
© Copyright 2012
American Mathematical Society
