TY - JOUR
TI - Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras
PY - 2023/06/01
Y2 - 2024/10/15
JF - Extracta Mathematicae
JA - Extr. Math.
VL - 38
IS - 1
SE - Algebras (associative, non associative, topological)
LA - English
DO - 10.17398/2605-5686.38.1.27
UR - https://doi.org/10.17398/2605-5686.38.1.27
SP - 27--50
AB - 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.
ER -