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ISSN 1088-6850(e) ISSN 0002-9947(p)

Isomorphism problems and groups of automorphisms for generalized Weyl algebras

Author(s): V. V. Bavula; D. A. Jordan
Journal: Trans. Amer. Math. Soc. 353 (2001), 769-794.
MSC (2000): Primary 16S36, 16W20, 16W35
Posted: 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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