Hom-Lie环幂零的条件  

Conditions for Nilpotency of Hom-Lie Rings

作　　者：贺婷婷 徐晓宁[1] HE Tingting;XU Xiaoning(School of Mathematics,Liaoning University,Shenyang 110036,China)

机构地区：[1]辽宁大学数学学院,沈阳110036

出　　处：《数学年刊（A辑）》2018年第4期391-406,共16页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11501274;No.11371182);辽宁省教育厅科学研究基金(No.L2015203)的资助

摘　　要：介绍并研究hom-Lie代数及hom-Lie环的幂零性.将线性映射α由一般的线性映射限制到研究α是对合映射的情形.通过建立Lie代数与hom-Lie代数间的关系,建立起Lie代数幂零和hom-Lie代数幂零间的联系.讨论了hom-Lie代数幂零的极大值子代数条件.此外,还研究了hom-Lie环幂零的正规化子条件和极大子代数条件.The aim of this paper is to introduce and study nilpotency of hom-Lie algebras and hom-Lie rings. The authors reduced the case where the twist map α is general linear map to the study of involutive hom-Lie algebras. This paper established a correspondence of nilpotency between Lie algebras and hom-Lie algebras. The maximal subalgebras condition for nilpotency of hom-Lie algebras is discussed. Moreover, the normalizer condition and the maximal subalgebras condition for nilpotency of hom-Lie rings are investigated.

关 键 词：hom-Lie代数 hom-Lie环 Noetherian环 极大子代数 

分 类 号：O152.5[理学—数学]