Strong (skew) xi-Lie commutativity preserving maps on algebras

被引：2

作者：

Gong, Lin ^{[1
]}

Qi, Xiaofei ^{[1
]}

Shao, Jie ^{[1
]}

Zhang, Feifei ^{[1
]}

机构：

[1] Shanxi Univ, Dept Math, Taiyuan 030006, Peoples R China

来源：

COGENT MATHEMATICS | 2015年 / 2卷

基金：

中国国家自然科学基金;

关键词：

algebras; xi-Lie products; skew xi-Lie products; commutativity;

D O I：

10.1080/23311835.2014.1003175

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let. be any unital *-algebra over the real or complex field F, and let xi is an element of F with xi not equal 1. Assume that Phi: A -> A is a map. It is shown that, Phi satisfies Phi(A) Phi(B) - xi Phi(B)Phi(A) = AB - xi BA for all A, B is an element of A if and only if Phi(I) is an element of Z(A), the center of A, Phi(I)(2) = I and Phi(A) = Phi(I)A for all A is an element of A; if Phi(I) = Phi(I)*, then Phi satisfies Phi(A)Phi(B) - xi Phi(B)Phi(A)* = AB - xi BA* for all A, B is an element of A if and only if Phi(I) is an element of Z(A), Phi(I)(2) = I and Phi(A) = Phi(I)A for all A is an element of A; if vertical bar xi vertical bar= 1 and Phi is surjective, then Phi satisfies Phi(A)Phi(B) - xi Phi(B)Phi(A)* = AB - xi BA* for all A, B is an element of A if and only if Phi(I) = Phi(I)* is an element of Z(A), Phi(I)(2) = I, and Phi(A) = Phi(I)A for all A is an element of A.

引用

页数：6

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