The Pozhidaev and Cantarini--Kac Constructions of Simple $n$-Lie Algebras: Distinctions and Realizations

Xinru Cao, Bakhrom A. Omirov, Yuhui Tan

Let $n\ge 3$, let $H\subseteq {\mathbb{C}}^n$ be any additive subgroup spanning ${\mathbb{C}}^n$, and let $0\ne t\in H$. We study Pozhidaev's central simple $n$-Lie algebra $P(H,t)=\wi…