Strong $k$-commutativity preserving maps on 2$\times$2 matrices

Meiyun Liu, Jinchuan Hou

Let ${\mathcal{M}}_2(\mathbb{F})$ be the algebra of 2$\times$2 matrices over the real or complex field $\mathbb{F}$. For a given positive integer $k\ge 1$, the $k$-commutator of $A$…