Hom-Lie环幂零的条件
Conditions for Nilpotency of Hom-Lie Rings

介绍并研究~hom{-}Lie代数及~hom{-}Lie环的幂零性. 将线性映射$\alpha$ 由一般的线性映射限制到研究$\alpha$ 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 $\alpha$ 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.