A note on Jordan-Kronecker invariants of semi-direct sums of sl(n) with a commutative ideal

Abstract

K. S. Vorushilov described Jordan-Kronecker invariants for semi-direct sums $\operatorname{sl} \ltimes \left(\mathbb{C}^n\right)^k$ if $k > n$ or if $n$ is a multiple of $k$. We describe the Jordan-Kronecker invariants in the cases $n \equiv \pm 1 \pmod k$.