Hom-Lie代数及其表示的注记

摘要

考虑Hom-Lie代数的结构、表示及上边缘算子的性质.对一般Hom-Lie代数,当映射β可逆时,其上的一系列上边缘算子对应的上同调群是同构的;对正规Hom-Lie代数,向量空间(ζ)上的Hom-Lie代数结构及Hom-Lie代数((ζ),[·,·],α)在向量空间V上的表示与∧(ζ)*(×)V上度数为1的算子以及算子所满足的性质是一一对应的.%The author considered properties of structures,representations and coboundary operators of Hom-Lie algebras.For general Hom-Lie algebras,whenβ was a reversible map,cohomology groups corresponding to a series of coboundary operators were isomorphic;for regular Hom-Lie algebras,there was a one to one relationship between the structure of Hom-Lie algebra ((ζ),[·,·],α) on vector space (ζ),the representation of ((ζ),[·,·],α) on vector space V and operator of degree 1 on ∧ (ζ)* (×)V with some properties.