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 $\mathrm{sl}⋉{\left({\mathbb{C}}^n\right)}^k$ if $k>n$ or if $n$ is a multiple of $k$. We describe the Jordan-Kronecker invariants in the cases $n\equiv \pm 1(\mathrm{mod}k)$.