@article{Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras_2023, volume={38}, url={https://revista-em.unex.es/index.php/EM/article/view/2605-5686.38.1.27}, DOI={10.17398/2605-5686.38.1.27}, abstractNote={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.}, number={1}, journal={Extracta Mathematicae}, year={2023}, month={Jun.}, pages={27–50} }