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

2023/06/13 by S. Launois, Launois, S., I. Oppong +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2306.07800

openalex publication_date 2023/06/13 · openalex created_date 2023/06/15 · openalex updated_date 2026/07/28

Abstract

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

Related

• Poisson and Hochschild cohomology and the semiclassical limit
• Semiquantum Geometry
• Poisson (co)homology of truncated polynomial algebras in two variables
• Hopf actions on Poisson algebras
• A natural map from a quantized space onto its semiclassical limit and a multi-parameter Poisson Weyl algebra