On the Structures of Hom-Lie Algebras

作     者：Shengxiang WANG Xiaohui ZHANG 

作者机构：School of Mathematics SciencesChuzhou UniversityAnhui 239000P. R. China Department of MathematicsSoutheast UniversityJiangsu 210096P. R. China 

出 版 物：《Journal of Mathematical Research with Applications》 (数学研究及应用(英文版))

年 卷 期：2014年第34卷第4期

页      面：459-466页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the Excellent Young Talents Fund Project of Anhui Province(Grant No.2013SQRL092ZD) the Natural Science Foundation of Anhui Province(Grant Nos.1408085QA06 1408085QA08) the Excellent Young Talents Fund Project of Chuzhou University(Grant No.2013RC001) the Research and Innovation Projectfor College Graduates of Jiangsu Province(Grant No.CXLX12-0071) 

主　　题：Hom-associative algebra Hom-Lie algebra Kegel’s theorem. 

摘      要：Let A be a multiplicative Hom-associative algebra and L a multiplicative Hom-Lie algebra together with surjective twisting maps. We show that if A is a sum of two commutative Hom-associative subalgebras, then the commutator Hom-ideal is nilpotent. Furthermore, we obtain an analogous result for Hom-Lie algebra L extending Kegel’s Theorem. Finally, we discuss the Hom-Lie ideal structure of a simple Hom-associative algebra A by showing that any non-commutative Hom-Lie ideal of A must contain [A, A].