This article is cited in 7 papers

Quasidifferential operator and quantum argument shift method

Y. Ikeda

Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia

Abstract: We describe an explicit formula for the first-order quasiderivation of an arbitrary central element of the universal enveloping algebra of a general linear Lie algebra. We apply it to show that derivations of any two central elements of the universal enveloping algebra commute. This contributes to the Vinberg problem of finding commutative subalgebras in universal enveloping algebras with the underlying Poisson algebras determined by the argument shift method.

Keywords: universal enveloping algebra, Lie algebra, quantum argument shift method, deformation quantization.

Received: 25.11.2021
Revised: 13.01.2022

DOI: 10.4213/tmf10212

 English version: Theoretical and Mathematical Physics, 2022, 212:1, 918–924

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