This article is cited in 16 papers

On Limits of Mishchenko–Fomenko Subalgebras in Poisson Algebras of Semisimple Lie Algebras

V. V. Shuvalov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In this paper, the commutative (with respect to the Poisson bracket) subalgebras in the Poisson algebras of the semisimple Lie algebras are considered on condition that these subalgebras are limits of Mishchenko–Fomenko subalgebras. We study the case of the degeneration within a fixed Cartan subalgebra. The structure of the limit subalgebras is described (i.e., it is proved that these subalgebras are free, and their generators are found). The classification of the limit subalgebras of the above type is also established.

Keywords: semisimple Lie algebra, Poisson algebra, commutative subalgebra, integrable Hamiltonian system.

UDC: 512.813.4

Received: 29.01.2002

DOI: 10.4213/faa219

 English version: Functional Analysis and Its Applications, 2002, 36:4, 298–305

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