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L_∞-derivations and the argument shift method for deformation quantization algebras

2019/12/02 by G. Sharygin, Sharygin, G.
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1912.00586

openalex publication_date 2019/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The argument shift method is a well-known method for generating commutative families of functions in Poisson algebras from central elements and a vector field, verifying a special condition with respect to the Poisson bracket. In this notice we give an analogous construction, which gives one a way to create commutative subalgebras of a deformed algebra from its center (which is as it is well known describable in the terms of the center of the Poisson algebra) and an L_∞-differentiation of the algebra of Hochschild cochains, verifying some additional conditions with respect to the Poisson structure.

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