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arXiv · 2508.03096

Cohomologies and linear deformations of relative Rota-Baxter operators on (pre-)Jacobi-Jordan algebras

Nabil Oro Djibril·Sylvain Attan
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Abstract

Some results on (pre-)Jacobi-Jordan algebras and their representations are proved. Moreover, the notion of matched pairs and relative Rota-Baxter operators on these algebras are introduced and studied. The cohomology theory of relative Rota-Baxter operators on (pre)-Jacobi-Jordan algebras is introduced. We use the cohomological approach to study linear deformations of relative Rota-Baxter operators. In particular, the notion of Nijenhuis elements is introduced to characterize trivial linear deformations.

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Nabil Oro Djibril, Sylvain Attan. 2025-08-05. Cohomologies and linear deformations of relative Rota-Baxter operators on (pre-)Jacobi-Jordan algebras. https://arxiv.org/abs/2508.03096

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