Maps on Mn preserving lie products

被引：0

作者：

Dolinar, Gregor ^{[1
]}

机构：

[1] Univ Ljubljana, Fac Elect Engn, SI-1000 Ljubljana, Slovenia

来源：

PUBLICATIONES MATHEMATICAE-DEBRECEN | 2007年 / 71卷 / 3-4期

关键词：

non-linear preserver problem; Lie product;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M-n be the Lie algebra of all n x n complex matrices with the Lie product [A, B] = AB - BA and let phi : M-n -> M-n satisfy phi([A, B]) = [phi(A), phi(B)], A, B is an element of M-n. Then phi(M-n) is a commutative subset of M-n or there exist an invertible matrix T is an element of M-n, a function phi : M-n -> C satisfying phi(C) = 0 for every trace zero matrix C is an element of M-n, and a homomorphism f of the complex field, such that phi([a(ij)]) = T[f(a(ij))]T-1 + phi([a(ij)])I for all [a(ij)] is an element of M-n, or phi([a(ij)]) = -T[f(a(ij))]T-t(-1) + phi([a(ij)])I for all [a(ij)] is an element of M-n.

引用

页码：467 / 477

页数：11