| 贺婷婷,徐晓宁.Hom-Lie环幂零的条件[J].数学年刊A辑,2018,(4):391~406 |
| Hom-Lie环幂零的条件 |
| Conditions for Nilpotency of Hom-Lie Rings |
| Received:December 02, 2016 Revised:July 05, 2017 |
| DOI：10.16205/j.cnki.cama.2018.0033 |
| 中文关键词: Hom-Lie algebra, Hom-Lie ring, Noetherian ring, Maximal subalgebra |
| 英文关键词:Hom-Lie algebra, Hom-Lie ring, Noetherian ring, Maximal subalgebra |
| 基金项目:本文受到国家自然科学基金(No.11501274,No.11371182)和辽宁省教育厅科学研究基金(No.L2015203)的资助. |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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. |
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