New techniques for calculation of Jordan-Kronecker invariants for Lie algebras and Lie algebra representations

2024/09/14 by И. К. Козлов, Kozlov, I. K.
Chemistry · #Molecular spectroscopy and chirality

paper · pdf · doi:10.48550/arxiv.2409.09535

Abstract

We introduce two novel techniques that simplify calculation of Jordan-Kronecker invariants for a Lie algebra \mathfrakg and for a Lie algebra representation ρ. First, the stratification of matrix pencils under strict equivalence puts restrictions on the Jordan-Kronecker invariants. Second, we show that the Jordan-Kronecker invariants of a semi-direct sum \mathfrakg \ltimes_ρ V are sometimes determined by the Jordan-Kronecker invariants of the dual Lie algebra representation ρ^*.

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