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Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras
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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.
Universidad de Extremadura - Servicio de Publicaciones
Title: Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras
Description:
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.
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