辛代数的极大幂零子代数的保李括积零的线性映射

Let F be a field with char F = 2, 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 ≥ 4, a map φ of l preserves zero Lie brackets in both directions if and only if φ = ψcσT0λαφdηf, where ψc,σT0,λα,φd,ηf are the standard maps preserving zero Lie brackets in both directions.

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

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.