|
Pure Mathematics 2020
BiHom-Jordan代数的表示
|
Abstract:
本文主要介绍了BiHom-Jordan代数的定义、表示和Ο-算子。首先,给出了BiHom-Jordan代数及其表示的定义和例子、BiHom-Jordan代数表示的等价条件,同时给出BiHom-Jordan代数表示的对偶映射是表示所满足的条件。其次,给出了BiHom-pre-Jordan代数的定义,找到BiHom-pre-Jordan代数与BiHom-Jordan代数之间的关系。最后,给出了BiHom-Jordan代数上的Ο-算子、Rota-Baxter算子的定义,以及BiHom-Jordan代数上的Ο-算子与BiHom-pre-Jordan代数之间的关系。
This article mainly introduces the definition, representation and Ο-operator of BiHom-Jordan algebra. Firstly, we give the definition of BiHom-Jordan algebra and its representation, the condi-tions for judging the representation of BiHom-Jordan algebra and an example of representation. At the same time, it is given that the dual mapping of BiHom-Jordan algebra representation is the condition that the representation satisfies. Secondly, we give the definition of BiHom-pre-Jordan algebra. The relation between BiHom-pre-Jordan algebra and BiHom-Jordan algebra is found. Final-ly, we give the definition of Ο-operator and Rota-Baxter operator on BiHom-Jordan algebra, and the relationship between Ο-operator on BiHom-Jordan algebra and BiHom-pre-Jordan algebra.
[1] | Albert, A.A. (1947) A Structure Theory for Jordan Algebras. Annals of Mathematics, 48, 446-467. |
[2] | Jacobson, N. (1968) Structure and Representations of Jordan Algebras. American Mathematical Society, Providence, Rhode Is-land. |
[3] | Braun, H. and Koecher, M. (1966) Jordan-Algebren. Springer-Verlag, Berlin. |
[4] | 候冬平. 预约当双代数和Loday代数的约当代数类似[D]: [博士学位论文]. 天津: 南开大学, 2010: 1-118. |
[5] | Hou, D.P. and Bai. C.M. (2013) Pre-Jordan Algebras. Mathematica Scandinavica, 112, 19-48. |
[6] | Chtioui, T., Mabrouk, S. and Makhlouf, A. (2018) BiHom-Alternative, BiHom-Malcev and BiHom-Jordan Algebras. arXiv:1811.10394 https://doi.org/10.1216/rmj.2020.50.69 |
[7] | Abdaoui, E.K., Ammar, F. and Makhlouf, A. (2017) Hom-Alternative, Hom-Malcev and Hom-Jordan Superalgebras. Bulletin of the Malaysian Mathematical Sciences Society, 40, 439-472. https://doi.org/10.1007/s40840-016-0323-5 |