Isomorphism problems and groups of automorphisms for generalized Weyl algebras

Bavula, V.; Jordan, D.

doi:10.1090/S0002-9947-00-02678-7

Isomorphism problems and groups of automorphisms for generalized Weyl algebras
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by V. V. Bavula and D. A. Jordan PDF

Trans. Amer. Math. Soc. 353 (2001), 769-794 Request permission

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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