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Homological smoothness and deformations of generalized Weyl algebras

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Abstract

It is an immediate conclusion from Bavula’s papers [1], [2] that if a generalized Weyl algebra A = k[z; λ, η, φ(z)] is homologically smooth, then the polynomial φ(z) has no multiple roots. We prove in this paper that the converse is also true. Moreover, formal deformations of A are studied when k is of characteristic zero.

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Authors and Affiliations

  1. Departement Wiskunde-Informatica Middelheimcampus, Universiteit Antwerpen, Middelheimlaan 1, 2020, Antwerpen, Belgium

    Liyu Liu

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  1. Liyu Liu
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Correspondence to Liyu Liu.

Additional information

The author acknowledges the support of the European Union for ERC grant No 257004-HHNcdMir.

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Liu, L. Homological smoothness and deformations of generalized Weyl algebras. Isr. J. Math. 209, 949–992 (2015). https://doi.org/10.1007/s11856-015-1242-0

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  • DOI: https://doi.org/10.1007/s11856-015-1242-0

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