Authors: Jovanović, Božidar 
Šukilović, Tijana
Vukmirović, Srđan
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Bogoyavlenski conjecture and classification of multiplicity free and almost multiplicity free subgroups
First page: 31
Related Publication(s): Book of Abstracts
Conference: XXI Geometrical Seminar, June 26 - July 2, 2022, Belgrade
Issue Date: 2022
Rank: M32
In [Bogoyavlenski, O.I.: Integrable Euler equations associated with
filtrations of Lie algebras, Mat. Sb. 121(163) (1983) 233–242] is
conjectured that if the Euler equations on a Lie algebra g0 are integrable,
then their certain extensions to semisimple lie algebras g related to the
filtrations of Lie algebras
g0 ⊂ g1 ⊂ g2 · · · ⊂ gn−1 ⊂ gn = g
are integrable as well.
In particular, by taking g0 = {0} and natural filtrations of so(n)
and u(n), we have Gel’fand-Cetlin integrable systems. We proved the
conjecture for filtrations of compact Lie algebras g: the system are
integrable in a noncommutative sense by means of polynomial integrals.
Various constructions of complete commutative polynomial integrals for
the system are also given.
In addition, related to commutative polynomial integrability, we
classify almost multiplicity free subgroups of compact simple Lie groups,
see [Guillemin, V and Sternberg, S.: Multiplicity-free spaces, J. Diff.
Geometry 19 (1984) 31–56], [Krämer, M.: Multiplicity free subgroups
of compact connected Lie groups. Arch. Math. 27 (1976) 28–36].
Publisher: Faculty of Mathematics, University of Belgrade

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