广义随机Jordan代数的Jordan导子

Jordan Derivation of Generalized Stochastic Jordan Algebra

设F是特征不为2的域, M(n,F)为域F上全体n×n阶矩阵构成的矩阵代数,α为Fn中非0列向量,令L (α)={A∈M(n,F) Aα=0}.证明L(α)为M(n,F)的一个Jordan子代数(称为广义随机Jordan代数),并证明L(α)的所有的Jordan导子都是内导子.

Let F be a field with char(F)≠2,M( n,F) be the matrix algebra consisting of all n×nmatrices over F,and let α be a n dimensional non-zero column vector over F. Denote L(α)={A ∈ M( n,F) Aα= 0}. This paper proves that L(α) is a Jordan subalgebra over F( called generalized stochastic Jordan algebra),and any Jordan derivation of L(α) is an inner derivation.