Hochschild homology and cohomology of generalized Weyl algebras

2001/09/04 by Marco A. Farinati, Farinati, Marco A., Andrea L. Solotar +3 · 1 citation
Mathematics · #16E40 #16E65 #16W70 #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT #msc:16E40 #msc:16E65 #msc:16W70

paper · pdf · doi:10.48550/arxiv.math/0109025

16 pages

arxiv created 2001/09/04 · arxiv updated 2009/11/30

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(sl₂), primitive quotients of U(sl₂), 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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