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arXiv · 2007.01078

Construction of Hom-Pre-Jordan algebras and Hom-J-dendriform algebras

Taoufik Chtioui·Sami Mabrouk·Abdenacer Makhlouf
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Abstract

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.

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BibTeXRIS

Taoufik Chtioui, Sami Mabrouk, Abdenacer Makhlouf. 2020-07-02. Construction of Hom-Pre-Jordan algebras and Hom-J-dendriform algebras. https://arxiv.org/abs/2007.01078

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