Nonlinear Lie derivations on upper triangular matrices

作者：Chen Lin; Zhang Jianhua^*

来源：Linear and Multilinear Algebra, 2008, 56(6): 725-730.

DOI：10.1080/03081080701688119

• nonlinear Lie derivation
• upper triangular matrix
• Lie product

Let M(n)(A) and T(n)(A) be the algebra of all n n matrices and the algebra of all n n upper triangular matrices over a commutative unital algebra , respectively. In this note we prove that every nonlinear Lie derivation from T(n)(A) into M(n)(A) is of the form A -> AT - TA + A(phi) + xi(A)I(n), where T is an element of M(n)(A), phi: A -> A is an additive derivation, xi:T(n)(A)-> A is a nonlinear map with xi(AB - BA) = 0 for all A, B is an element of T(n)(A) and A(phi) is the image of A(phi) under applied entrywise.

• 出版日期2008
• 单位陕西师范大学