Poisson derivations of a semiclassical limit of a family of quantum second Weyl algebras. (English) Zbl 07787758
The authors continue their recent research [S. Launois and I. Oppong, Bull. Sci. Math. 184, Article ID 103257, 43 p. (2023; Zbl 1529.16025)], where they describe deformations \(\mathcal A_{\alpha,\beta}\) of the second Weyl algebra and compute their derivations. More precisely, they identify the semiclassical limits \(\mathcal A_{\alpha,\beta}\) of these deformations and calculate their Poisson derivations. As a consequence, it turns out that the first Hochschild cohomology group \(\mathrm{HH^1}(\mathcal A_{\alpha,\beta})\) is isomorphic to the first Poisson cohomology group \(\mathrm{HP^1}(\mathcal A_{\alpha,\beta})\). The authors raise the question whether this is also true for higher cohomology groups.
Reviewer: Aleksandr G. Aleksandrov (Moskva)
MSC:
| 16S30 | Universal enveloping algebras of Lie algebras |
| 16T20 | Ring-theoretic aspects of quantum groups |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 53D55 | Deformation quantization, star products |
Keywords:
quantum second Weyl algebras; deformations; semiclassical limits; quantization; Poisson derivations; Poisson algebras; Poisson primitive ideals; Hochschild cohomology; Poisson cohomology; quantized enveloping algebras; Poisson-Ore extensionCitations:
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