Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2011, Number 1, Pages 31–36 (Mi vmumm652)  
Mathematics

Maximal commutative subalgebras of functions on spaces dual to Lie algebras

M. M. Derkacha, A. S. Tenb

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Yandex company, Moscow
Full-text PDF (363 kB)
Abstract: The problem of searching the maximal commutative sets of polynomial functions on the dual space to the semidirect sum of a Lie algebra and a vector space is studied. It is proved that if the first component of the semidirect sum is a compact algebra, then the set of functions can be described explicitly. This result is applied to some particular Lie algebras.
Key words: Lie–Poisson bracket, Liouville theorem, Mishchenko–Fomenko conjecture, complete commutative sets of polynomials.
Received: 16.06.2010
English version:
Moscow University Mathematics Bulletin, 2011, Volume 66, Issue 1, Pages 30–34
DOI: https://doi.org/10.3103/S0027132211010062
Bibliographic databases:
Document Type: Article
UDC: 514.745.82
Language: Russian
Citation: M. M. Derkach, A. S. Ten, “Maximal commutative subalgebras of functions on spaces dual to Lie algebras”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011, no. 1, 31–36; Moscow University Mathematics Bulletin, 66:1 (2011), 30–34
Citation in format AMSBIB
\Bibitem{DerTen11}
\by M.~M.~Derkach, A.~S.~Ten
\paper Maximal commutative subalgebras of functions on spaces dual to Lie algebras
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2011
\issue 1
\pages 31--36
\mathnet{http://mi.mathnet.ru/vmumm652}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2848767}
\zmath{https://zbmath.org/?q=an:1304.17015}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2011
\vol 66
\issue 1
\pages 30--34
\crossref{https://doi.org/10.3103/S0027132211010062}
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