关于上三角矩阵代数之间经典伴随交换单射

On classical adjoint-commuting injective mappings between upper triangular matrix algebras

令F是一个域,且|F|>n+1,m,n为整数且m,n≥3.Tn(T_m)(F)是F上所有n×n(m×m)上三角矩阵的集合.本文中,刻画了从T_n(F)到T_m(F)的保经典伴随交换的单映射,给出了映射的表达式,对相应的方阵的工作是一个新的补充,所用方法是将其化归为相应的线性保持问题.

Let F be a field and let m and n be integers with m, n ≥ 3, Tn（Tm）（F） be the set of all n × n（m × m） upper triangular matrices over F. This paper describes a induced map preserving classical adjoint-commuting injective mappings from Tn （F） to Tm （F）, gives expressions of the map, adds the work of relevant square matrix. This paper use ways of translating the problem into relevant linear preserving problems.