Hom-李代数的子代数
Algebras of quotients of Hom-Lie algebras
摘要：
本文引入了Hom-李代数的子代数的概念，研究了Hom-李代数提升到其子代数的一些性质.给出了Hom-李代数具有同元代数的一些充要条件。我们还研究了一个Hom-李代数和由相应的Hom-李代数的内导子生成的结合代数之间的关系。此外，我们还引入了稠密扩张的概念，并通过稠密扩张得到了关于同素元的Hom-李代数的一个命题。
英文摘要：
In this paper, we introduce the notion of algebras of quotients of Hom-Lie algebras and investigate some properties which can be lifted from a Hom-Lie algebra to its algebra of quotients. We also give some necessary and sufficient conditions for Hom-Lie algebras having algebras of quotients. We also examine the relationship between a Hom-Lie algebra and the associative algebra generated by inner derivations of the corresponding Hom-Lie algebra of quotients. Moreover, we introduce the notion of dense extensions and get a proposition about Hom-Lie algebras of quotients via dense extensions.
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