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Poisson derivations of a semiclassical limit of a family of quantum second Weyl algebras (2306.07800v1)
Published 13 Jun 2023 in math.RA and math.QA
Abstract: In previous paper, we studied deformations $A_{\alpha,\beta}$ of the second Weyl algebra and computed their derivations. In the present paper, we identify the semiclassical limits $\mathcal{A}{\alpha,\beta}$ of these deformations and compute their Poisson derivations. Our results show that the first Hochschild cohomology group HH$1(A{\alpha,\beta})$ is isomorphic to the first Poisson cohomology group HP$1( \mathcal{A}_{\alpha,\beta}).$