辛代数的极大幂零子代数的保李括积零的线性映射

Maps Preserving Zero Lie Brackets on a Maximal Nilpotent Subalgebra of the Symplectic Algebra

中文关键词:  极大幂零子代数  李括积零  辛代数.

英文关键词:maximal nilpotent subalgebra  zero Lie brackets  symplectic algebra.

中文摘要:

      令$F$表示特征不等于2的域, $l$表示辛代数$sp(2m,F)$的一个极大幂零子代数. 本文刻画了$l$的双向保李括积零的线性映射, 证明了当$m\geq 4$时, $l$的一个线性映射$\varphi$是双向保李括积零的当且仅当$\varphi=\psi_{c}\sigma_{t}\lambda_{\alpha}\phi_{d}\eta_{f}$, 这里$\psi_{c}, \sigma_{t}, \lambda_{\alpha}, \phi_{d}, \eta_{f}$ 都是双向保李括积零的标准映射.

英文摘要:

      Let $F$ be a field with char $F\neq2$, $l$ a maximal nilpotent subalgebra of the symplectic algebra $\sp(2m,F)$. In this paper, we characterize linear maps of $l$ which preserve zero Lie brackets in both directions. It is shown that for $m\geq 4$, a map $\varphi$ of $l$ preserves zero Lie brackets in both directions if and only if $\varphi=\psi_{c}\sigma_{T_0}\lambda_{\alpha}\phi_{d}\eta_{f}$, where $\psi_{c}, \sigma_{T_0}, \lambda_{\alpha}, \phi_{d}, \eta_{f}$ are the standard maps preserving zero Lie brackets in both directions.