%0 Journal Article
%T 相容BiHom-李代数的表示及BiHom-李代数的形变<br>Representation of Compatible BiHom-Lie Algebra and Deformation of BiHom-Lie Algebra
%A 孙尧
%J Advances in Applied Mathematics
%P 3780-3787
%@ 2324-8009
%D 2022
%I Hans Publishing
%R 10.12677/AAM.2022.116405
%X 本文主要研究相容BiHom-李代数的表示与BiHom-李代数的形变。首先给出了相容BiHom-李代数的定义，找到判断两个BiHom-李代数是相容的方法。其次定义了相容BiHom-李代数的表示，得到了相容BiHom-李代数与其表示空间的直和上存在相容BiHom-李代数结构的条件，并给出了相容BiHom-李代数表示的例子。然后讨论了相容BiHom-李代数表示的对偶映射同样是该相容BiHom-李代数表示所满足的条件，并构造出了对偶表示。最后构造了BiHom-李代数的形变。<br />
In this paper, we mainly discuss the representation of BiHom-Lie algebra and the deformation of BiHom-Lie algebra. Firstly, we give the definition of compatible BiHom-Lie algebra and the method of judging the compatibility of two BiHom-Lie algebras. Secondly, we define the representation of compatible BiHom-Lie algebra, and get the conditions for the existence of compatible BiHom-Lie al-gebra structure on the direct sum of the compatible BiHom-Lie algebra and its representation space. We also give an example of the representation of compatible BiHom-Lie algebra. Then we give the conditions when the dual mapping of the representation of compatible BiHom-Lie algebra is also the representation of compatible BiHom-Lie algebra and constructs the dual representation of the representation of compatible BiHom-Lie algebra. Finally, we introduce the deformation of Bi-Hom-Lie algebra.
%K BiHom-李代数，相容BiHom-李代数，表示，形变<br>BiHom-Lie Algebra
%K Compatible BiHom-Lie Algebra
%K Representation
%K Deformation
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=52815