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Isomorphism problems and groups of automorphisms for generalized Weyl algebras


Authors: V. V. Bavula and D. A. Jordan
Journal: Trans. Amer. Math. Soc. 353 (2001), 769-794
MSC (2000): Primary 16S36, 16W20, 16W35
DOI: https://doi.org/10.1090/S0002-9947-00-02678-7
Published electronically: October 13, 2000
MathSciNet review: 1804517
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Abstract:

We present solutions to isomorphism problems for various generalized Weyl algebras, including deformations of type-A Kleinian singularities and the algebras similar to $U(\mathfrak{sl}_2)$introduced by S. P. Smith. For the former, we generalize results of Dixmier on the first Weyl algebra and the minimal primitive factors of $U(\mathfrak{sl}_2)$ by finding sets of generators for the group of automorphisms.


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Additional Information

V. V. Bavula
Affiliation: Department of Mathematics and Computer Science, University of Antwerp, U. I. A., B-2610 Wilrijk, Belgium
Address at time of publication: Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom
Email: v.bavula@sheffield.ac.uk

D. A. Jordan
Affiliation: Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom
Email: d.a.jordan@sheffield.ac.uk

DOI: https://doi.org/10.1090/S0002-9947-00-02678-7
Keywords: Isomorphism, generalized Weyl algebra, skew polynomial ring, automorphism group, Kleinian singularity
Received by editor(s): July 12, 1999
Published electronically: October 13, 2000
Additional Notes: This work was done during visits to the University of Sheffield by the first author with the support of the London Mathematical Society
Article copyright: © Copyright 2000 American Mathematical Society

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