论文标题
Bihom-Post-Lie代数的构建和表示理论
Constructions and representation theory of BiHom-post-Lie algebras
论文作者
论文摘要
本文的主要目的是给出BIHOM-POST-LIE代数的一些构建结果，这是对lie-orgebras和Hom-Post-Lie代数的概括。它们是$ \ Mathcal {O} $ - Bihom-Lie代数的运营商背后的代数结构。它们也可以被视为分裂成Bihom-Lie-Algebra结构的三个部分。此外，我们在矢量空间$ v $上开发了Bihom-Post-Lie代数的表示理论。我们表明，自然存在其次级谎言代数的诱发代表。
The main goal of this paper is to give some construction results of BiHom-post-Lie algebras which are a generalization of both post-Lie-algebras and Hom-post-Lie algebras. They are the algebraic structures behind the $\mathcal{O}$-operator of BiHom-Lie algebras. They can be also regarded as the splitting into three parts of the structure of a BiHom-Lie-algebra. Moreover we develop the representation theory of BiHom-post-Lie algebras on a vector space $V$. We show that there is naturally an induced representation of its sub-adjacent Lie algebra.
