论文标题
霍姆 - 约旦代数和霍姆·尼古拉形式代数的构建
Construction of Hom-Pre-Jordan algebras and Hom-J-dendriform algebras
论文作者
论文摘要
这项工作的目的是介绍和研究Hom-Pre-Jordan代数和Hom-J-Dendriform代数的概念，该代数概括了Hom-Jordan代数。 Hom-Pre-Jordan代数被认为是Rota-Baxter操作员之后的Hom-Jordan代数的基础代数结构，以及本文介绍的$ \ Mathcal {O} $ - 运算符。霍姆 - 约旦代数也是霍姆 - 约旦代数代数的类似物。 Hom-Pre-Jordan代数的抗换向器是Hom-Jordan代数，左乘法操作员表示了霍姆 - 约旦代数的表示。另一方面，HOM-J dendriform代数是Hom-Jordan代数类似物的代数类似物，使得两个操作的抗官员是Hom-Pre-Jordan代数。
The aim of this work is to introduce and study the notions of Hom-pre-Jordan algebra and Hom-J-dendriform algebra which generalize Hom-Jordan algebras. Hom-Pre-Jordan algebras are regarded as the underlying algebraic structures of the Hom-Jordan algebras behind the Rota-Baxter operators and $\mathcal{O}$-operators introduced in this paper. Hom-Pre-Jordan algebras are also analogues of Hom-pre-Lie algebras for Hom-Jordan algebras. The anti commutator of a Hom-pre-Jordan algebra is a Hom-Jordan algebra and the left multiplication operator gives a representation of a Hom-Jordan algebra. On the other hand, a Hom-J-dendriform algebra is a Hom-Jordan algebraic analogue of a Hom-dendriform algebra such that the anti-commutator of the sum of the two operations is a Hom-pre-Jordan algebra.
