Nonlinear Lie derivations on upper triangular matrices

被引：47

作者：

Chen, Lin ^{[1
]}

Zhang, Jianhua ^{[1
]}

机构：

[1] Shaanxi Normal Univ, Coll Math & Informat Sci, Xian 710062, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2008年 / 56卷 / 06期

基金：

中国国家自然科学基金;

关键词：

nonlinear Lie derivation; upper triangular matrix; Lie product;

D O I：

10.1080/03081080701688119

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：725 / 730

页数：6

共 5 条

[1] Lie derivations of triangular algebras [J].

Cheung, WS .

LINEAR & MULTILINEAR ALGEBRA, 2003, 51 (03) :299-310

[2] Maps on upper triangular matrices preserving Lie products [J].

Dolinar, Gregor .

LINEAR & MULTILINEAR ALGEBRA, 2007, 55 (02) :191-198

[3] Symmetric amenability and the nonexistence of Lie and Jordan derivations [J].

Johnson, BE .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1996, 120 :455-473

[4] The structure of Lie derivations on C*-algebras [J].

Mathieu, M ;

Villena, AR .

JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 202 (02) :504-525

[5]

[张建华 Zhang Jianhua], 2003, [数学学报, Acta Mathematica Sinica], V46, P657

← 1 →