Poisson derivations of a semiclassical limit of a family of quantum second Weyl algebras

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In [16], we studied deformations Aα,β of the second Weyl algebra and computed their derivations. In the present paper, we identify the semiclassical limits Aα,β of these deformations and compute their Poisson derivations. Our results show that the first Hochschild cohomology group HH1(Aα,β) is isomorphic to the first Poisson cohomology group HP1(Aα,β).