X. F. Qi
Department of Mathematics, Shanxi University, Taiyuan 030006, P. R. China.
[ 1 ] - $k$-power centralizing and $k$-power skew-centralizing maps on triangular rings
Let $\mathcal A$ and $\mathcal B$ be unital rings, and $\mathcal M$ be an $(\mathcal A, \mathcal B)$-bimodule, which is faithful as a left $\mathcal A$-module and also as a right $\mathcal B$-module. Let ${\mathcal U}=Tri(\mathcal A, \mathcal M, \mathcal B)$ be the triangular ring and ${\mathcal Z}({\mathcal U})$ its center. Assume that $f:{\mathcal U}\rightarrow{\mathcal U}$ is a map satisfying …
[ 2 ] - Nonlinear $*$-Lie higher derivations on factor von Neumann algebras
Let $\mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation $D={\phi_{n}}_{n\in\mathbb{N}}$ on $\mathcal M$ is additive. In particular, if $\mathcal M$ is infinite type $I$ factor, a concrete characterization of $D$ is given.