BiHom-Jordan代数的表示
Representation of BiHom-Jordan Algebra
摘要:
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。
Abstract:
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.
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