This article is cited in 9 papers

Uniqueness of liftings of maximal commutative subalgebras of the Poisson–Lie algebra to the enveloping algebra

A. A. Tarasov

M. V. Lomonosov Moscow State University

Abstract: It is proved that each generalized Mishchenko–Fomenko subalgebra of the Poisson algebra of the Lie algebra ${{\mathfrak{gl}}_n({\mathbb C})}$ can be lifted to a unique commutative subalgebra of the enveloping algebra.

UDC: 519.46

MSC: 17B35, 17B63

Received: 20.01.2003

DOI: 10.4213/sm757

 English version: Sbornik: Mathematics, 2003, 194:7, 1105–1111

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