|
Maximal Commutative Subalgebras of Functions on Spaces Dual to Lie Algebras / Derkach M.M. and Ten A.S. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. № 1. P. 31-36 [Moscow Univ. Math. Bulletin. Vol. 66, No 1, 2011. P. 30-34]. 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 semi-direct 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.
|