D_m 型正交代数的极大幂零子代数上保零李括积的映射（英文）

MAPS PRESERVING ZERO LIE BRACKETS ON A MAXIMAL NILPOTENT SUBALGEBRA OF THE ORTHOGONAL LIE AIGEBRA OF D_m TYPE

令F表示任意域,l_(2m)(F)表示F上D_m型正交李代数的极大幂零子代数.本文的目的是当m≥5时,刻画l_(2m)(F)上的每一个双向保零李括积的映射.利用文献[7]的主要结果和矩阵计算技巧,本文证明了l_(2m)(F)上的一个线性映射φ是双向保零李括积的当且仅当φ能够写成内自同构,图自同构,广义的对角自同构,中心映射,次中心自同构,极端映射和标量乘法的乘积.这推广了文献[7]的主要结果.

Let F be a field, l2m（F） a maximal nilpotent subalgebra of the orthogonal Lie algebra of Dm type. The aim of this paper is to characterize every linear map of l2m （F） which preserves zero Lie brackets in both directions when m 〉 5. By using the main theorem of the paper [7] and the skill of matrix computation, it is proved that a linear map φ of l2m（F） preserves zero Lie brackets in both directions if and only if φ is the product of an inner automorphism, a graph automorphism, a generalized diagonal automorphism, a central map, a sub-central automorphism, an extremal map and a scalar multiplication. This extends the main result of the paper [7].