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Hochschild homology and cohomology of generalized Weyl algebras

Marco A. Farinati·Andrea L. Solotar·Mariano Suarez-Alvarez
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Abstract

We compute Hochschild homology and cohomology of a class of generalized Weyl algebras (for short GWA, defined by Bavula in St.Petersbourg Math. Journal 1999 4(1) pp. 71-90). Examples of such algebras are the n-th Weyl algebras, U(sl_2), primitive quotients of U(sl_2), and subalgebras of invariants of these algebras under finite cyclic groups of automorphisms. We answer a question of Bavula - Jordan (Trans. A.M.S. 353 (2) 2001 pp. 769 -794) concerning the generator of the group of automorphism of a GWA. We also explain previous results on the invariants of Weyl algebras and of primitive quotients.

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Marco A. Farinati, Andrea L. Solotar, Mariano Suarez-Alvarez. 2001-09-04. Hochschild homology and cohomology of generalized Weyl algebras. https://arxiv.org/abs/math/0109025

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