|
|
相容BiHom-李代数的表示及BiHom-李代数的形变
|
Abstract:
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。
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.
| [1] | Graziani, G., Makhlouf, A., Menini, C. and Panaite, F. (2015) BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras. Symmetry Integrability and Geometry: Methods and Applications, 11, 11-34.
https://doi.org/10.3842/SIGMA.2015.086 |
| [2] | Saadaoui, N. (2021) Split Extensions of BiHom-Lie Algebras. arXiv:2112.11995. |
| [3] | Cheng, Y.S. and Qi, H.G. (2022) Representations of BiHom-Lie algebras. Algebra Colloquium, 29, 125-142. |
| [4] | Liu, J., Sheng, Y. and Bai, C. (2021) Maurer-Cartan Characterizations and Cohomologies of Com-patible Lie Algebras. arXiv:2102.04742. |
| [5] | Das, A. (2022) Cohomology and Deformations of Compatible Hom-Lie Algebras. arXiv:2202.03137. |
| [6] | 李艳朋. BiHom-pre-Lie代数的双模[D]: [硕士学位论文]. 大连: 辽宁师范大学, 2020. |
