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

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.