Hochschild homology and cohomology of generalized Weyl algebras

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

Annales de l'Institut Fourier, Tome 53 (2003) no. 2, pp. 465-488.

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.

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, $𝒰\left(𝔰{𝔩}_2\right)$, primitive quotients of $𝒰\left(𝔰{𝔩}_2\right)$, 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

Classification : 16E40, 17B37, 16S32
Keywords: Hochschild cohomology, generalized Weyl algebras, automorphism group
Mot clés : cohomologie de Hochschild, algèbres de Weyl généralisées, groupe d'automorphismes

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