Geodesic
On Limits of Mishchenko--Fomenko Subalgebras in Poisson Algebras of Semisimple Lie Algebras
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 4, pp. 55-64

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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, integrable Hamiltonian system.
Mots-clés : Poisson algebra, commutative subalgebra 
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     author = {V. V. Shuvalov},
     title = {On {Limits} of {Mishchenko--Fomenko} {Subalgebras} in {Poisson} {Algebras} of {Semisimple} {Lie} {Algebras}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {55--64},
     publisher = {mathdoc},
     volume = {36},
     number = {4},
     year = {2002},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2002_36_4_a4/}
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V. V. Shuvalov. On Limits of Mishchenko--Fomenko Subalgebras in Poisson Algebras of Semisimple Lie Algebras. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 4, pp. 55-64. http://geodesic.mathdoc.fr/item/FAA_2002_36_4_a4/