Deformations of relative Rota-Baxter operators on Hom-Jacobi-Jordan algebras

2023/08/08 by Jules Anitheou, Anitheou, Jules, Sylvain Attan +3
Computer Science · Mathematics · #16W10 #17A30 #17B10 #17B56 #17C50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2308.04203

openalex publication_date 2023/08/08 · openalex created_date 2023/08/10 · openalex updated_date 2026/07/28

Abstract

Representations of Hom-Jacobi-Jordan algebras are studied. In particular, adjoint representations and trivial representations are studied in detail. Derivations and central extensions of Hom-Jacobi-Jordan algebras are also discussed as an application. Morover, we introduce the cohomology theory on Hom-Jacobi-Jordan algebras as well as the one of relative Rota-Baxter operators on Hom-Jacobi-Jordan algebras. Finally, we use the cohomological approach to study deformations of Hom-Jacobi-Jordan algebras and those of relative Rota-Baxter operators.

Related

• Cohomologies and linear deformations of relative Rota-Baxter operators on (pre-)Jacobi-Jordan algebras
• Representations of weighted Rota-Baxter Jacobi-Jordan algebras
• Representations and O-operators of Hom-(pre)-Jacobi-Jordan algebras
• Representations and relative Rota-Baxter operators of Hom-Leibniz Poisson algebras
• Twisted Rota-Baxter family operators on Hom-associative algebras