Homological smoothness and deformations of generalized Weyl algebras
Abstract
It is an immediate conclusion from Bavula's papers Bavula:GWA-def, Bavula:GWA-tensor-product that if a generalized Weyl algebra A=[z;λ,η,(z)] is homologically smooth, then the polynomial (z) has no multiple roots. We prove in this paper that the converse is also true. Moreover, formal deformations of A are studied when is of characteristic zero.
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