$L_{\infty }$-derivations and the argument shift method for deformation quantization algebras

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 $L_{\infty }$-differentiation of the algebra of Hochschild cochains, verifying some additional conditions with respect to the Poisson structure.

Few minor misprints are corrected, new reference added. Submitted to Acta Mathematica Spalatensia

References in corpus (2)

• Quantization of the Gaudin System
• Generalized argument shift method and complete commutative subalgebras in polynomial Poisson algebras