Cohomologies and deformations of Hom-Jacobi-Jordan algebras and relative Rota-Baxter operators
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https://doi.org/10.17398/Palabras clave:
Hom-Jacobi-Jordan algebra, relative Rota-Baxter operator, cohomology, deformationResumen
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.
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