Abstract
We give a criterion of (micro-)kroneckerity of the linear Poisson pencil on g ∗ related to an algebraic Nijenhuis operator N : g → g 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 gl n .
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