Algebraic Nijenhuis operators and Kronecker Poisson pencils |
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| Authors: | Andriy Panasyuk |
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| Affiliation: | a Division of Mathematical Methods in Physics, University of Warsaw, Ho?a St. 74, 00-682 Warsaw, Poland
b Pidstrygach Institute of Applied Problems of Mathematics and Mechanics, Naukova St. 3b, 79601 Lviv, Ukraine |
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| Abstract: | We give a criterion of (micro-)kroneckerity of the linear Poisson pencil on g∗ related to an algebraic Nijenhuis operator  on a finite-dimensional Lie algebra g. As an application we get a series of examples of completely integrable systems on semisimple Lie algebras related to Borel subalgebras and a new proof of the complete integrability of the free rigid body system on gln. |
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| Keywords: | 58F07 53A60 |
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