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Funktsional'nyi Analiz i ego Prilozheniya, 2002, Volume 36, Issue 4, Pages 55–64
DOI: https://doi.org/10.4213/faa219 (Mi faa219) 		 
This article is cited in 15 scientific papers (total in 15 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
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DOI: https://doi.org/10.4213/faa219
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.
Received: 29.01.2002
English version:
Functional Analysis and Its Applications, 2002, Volume 36, Issue 4, Pages 298–305
DOI: https://doi.org/10.1023/A:1021713927119
Bibliographic databases:
Document Type: Article
UDC: 512.813.4
Language: Russian
Citation: V. V. Shuvalov, “On Limits of Mishchenko–Fomenko Subalgebras in Poisson Algebras of Semisimple Lie Algebras”, Funktsional. Anal. i Prilozhen., 36:4 (2002), 55–64; Funct. Anal. Appl., 36:4 (2002), 298–305
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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