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Maximal commutative subalgebras of functions on spaces dual to Lie algebras

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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 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.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    M. M. Derkach & A. S. Ten

  2. “Yandex,”, Lev Tolstoi st. 16, Moscow, 119021, Russia

    M. M. Derkach & A. S. Ten

Authors
  1. M. M. Derkach
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  2. A. S. Ten
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Additional information

Original Russian Text © M.M. Derkach, A.S. Ten, 2011, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2011, Vol. 66, No. 1, pp. 31–36.

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Derkach, M.M., Ten, A.S. Maximal commutative subalgebras of functions on spaces dual to Lie algebras. Moscow Univ. Math. Bull. 66, 30–34 (2011). https://doi.org/10.3103/S0027132211010062

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  • DOI: https://doi.org/10.3103/S0027132211010062

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