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Abstract <p>We introduce two novel techniques that simplify calculation of Jordan–Kronecker invariants for a Lie algebra and for a Lie algebra representation. 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 of a Lie algebra with a commutative ideal are sometimes determined by the Jordan–Kronecker invariants of the dual Lie algebra representation.</p>

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New Techniques for Calculation of Jordan–Kronecker Invariants for Lie Algebras and Lie Algebra Representations

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • I. K. Kozlov

摘要

Abstract

We introduce two novel techniques that simplify calculation of Jordan–Kronecker invariants for a Lie algebra and for a Lie algebra representation. 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 of a Lie algebra with a commutative ideal are sometimes determined by the Jordan–Kronecker invariants of the dual Lie algebra representation.