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

• T. Chtioui ^[1] ; S. Mabrouk ^[2] ; A. Makhlouf ^[3]
  1. [1] University of Sfax

     University of Sfax

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  2. [2] University of Gafsa

     University of Gafsa

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  3. [3] Université de Haute Alsace, IRIMAS - Département de Mathématiques F-68093 Mulhouse, France

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• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 38, Nº 1, 2023, págs. 27-50
• Idioma: inglés
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  • 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 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.