Representations and O-operators of Hom-(pre)-Jacobi-Jordan algebras
Sylvain Attan
TL;DR
This paper introduces and studies representations and O-operators of Hom-(pre)-Jacobi-Jordan algebras, exploring their algebraic structures, matched pairs, and Nijenhuis operators to advance understanding of these mathematical objects.
Contribution
It presents new concepts and properties of Hom-(pre)-Jacobi-Jordan algebras, including representations, O-operators, matched pairs, and Nijenhuis operators, with various constructions.
Findings
Anticommutator of a Hom-pre-Jacobi-Jordan algebra forms a Hom-Jacobi-Jordan algebra
Left multiplication operator provides a representation of Hom-Jacobi-Jordan algebra
Various constructions of Hom-(pre)-Jacobi-Jordan algebras are obtained
Abstract
Representations and O-operators of Hom-(pre)-Jacobi-Jordan algebras are introduced and studied. The anticommutator of a Hom-pre-Jacobi-Jordan algebra is a Hom-Jacobi-Jordan algebra and the left multiplication operator gives a representation of a Hom-Jacobi-Jordan algebra. The notion of matched pairs and Nijenhuis operators of Hom-(pre)-Jacobi-Jordan algebras are given and various relevant constructions are obtained.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons