论文标题
在hom-lie代数上进行竞标和通勤线性地图
Biderivations and commuting linear maps on Hom-Lie algebras
论文作者
论文摘要
本文的目的是确定偏斜的biderivations $ \ text {bider} _ {\ text {s}}}（l，v）$和通勤线性映射映射$ \ text {com}（com}（l，v）$在hom-lie algebra $（l，α）$上的$（l，α）$（l，α）$（ β）$，两者都与$ \ text {cent}（l，v）$，$（v，ρ，β）$密切相关。具体而言，在适当的假设下，每一个$δ\ in \ text {bider} _ {\ text {s}}}（l，v）$是$δ（x，y）=β^{ - 1}γ（ - 1}γ（[x，y]）$的$ umugumutimumutimumutimut pext { - 1}γ{ - 1}γ（[x，y]）$与$ \ text {cent}（l，v）$重合。此外，我们给出了用于描述$ \ text {bider} _ {\ text {s}}}（l，v）$和$ \ text {com}（l，v）$的算法，并提供了几个示例。
The purpose of this paper is to determine skew-symmetric biderivations $\text{Bider}_{\text{s}}(L, V)$ and commuting linear maps $\text{Com}(L, V)$ on a Hom-Lie algebra $(L,α)$ having their ranges in an $(L,α)$-module $(V, ρ, β)$, which are both closely related to $\text{Cent} (L, V)$, the centroid of $(V, ρ, β)$. Specifically, under appropriate assumptions, every $δ\in\text{Bider}_{\text{s}}(L, V)$ is of the form $δ(x,y)=β^{-1}γ([x,y])$ for some $γ\in \text{Cent} (L, V)$, and $\text{Com}(L, V)$ coincides with $\text{Cent} (L, V)$. Besides, we give the algorithm for describing $\text{Bider}_{\text{s}}(L, V)$ and $\text{Com}(L, V)$ respectively, and provide several examples.
