保幂零元子代数的线性映射(英文)

Linear Maps That Preserve Lie Subalgebras of Nilpotent Elements

令L表示任意域上的C_m型或D_m李代数.线性映射?被称为是保幂零元子代数的,若?将每一个幂零元子代数映为另一个幂零元子代数.利用矩阵计算技巧和已知结论刻画了L的每一个保幂零元子代数的线性映射,推广了已有结论.

Let L be the Lie algebra of C_mor D_mtype over an arbitrary filed. A linear map Φ is said to preserve Lie subalgebras of nilpotent elements if Φ maps every subalgebra of nilpotent elements to some subalgebra of nilpotent elements. By using the skill of matrix computation and the known result, every linear map which preserves subalgebras of nilpotent elements of L is characterized.