Hochschild homology and cohomology of generalized Weyl algebras

[Homologie et cohomologie de Hochschild des algèbres de Weyl généralisées]

Farinati, Marco A. ; Solotar, Andrea L. ; Suárez-Álvarez, Mariano

Annales de l'Institut Fourier, Tome 53 (2003), p. 465-488 / Harvested from Numdam

Résumé

Nous calculons l'homologie et la cohomologie de Hochschild des algèbres de Weyl généraliseés introduites par V. Bavula. Nous répondons à une question de Bavula-Jordan concernant les générateurs du groupe d'automorphismes d'une telle algèbre. Ce calcul explique aussi des résultats connus sur les invariants des algèbres de Weyl et des quotients primitifs.

Abstract

We compute Hochschild homology and cohomology of a class of generalized Weyl algebras, introduced by V. V. Bavula in St. Petersbourg Math. Journal, 4 (1) (1999), 71-90. Examples of such algebras are the n-th Weyl algebras, ${\mathcal {U}}({\mathfrak {s}}{\mathfrak {l}}_2)$, primitive quotients of ${\mathcal {U}}({\mathfrak {s}}{\mathfrak {l}}_2)$, 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), 769-794) concerning the generators of the group of automorphisms of a generalized Weyl algebra. We also explain previous results on the invariants of Weyl algebras and of primitive quotients

Détail

Publié le : 2003-01-01

Zbl 1100.16008 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.1950
Classification:  16E40,  17B37,  16S32
Mots clés: cohomologie de Hochschild, algèbres de Weyl généralisées, groupe d'automorphismes

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