Representations of weighted Rota-Baxter Jacobi-Jordan algebras

2025/08/12 by Anitchéou, Jules, Attan, Sylvain
#16W10 #17B56 #17C50 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.09394

Abstract

Weighted Rota-Baxter Jacobi-Jordan algebras and their representations are studied. Moreover, we consider weighted Rota-Baxter paired operators that are related to weighted Rota-Baxter Jacobi-Jordan algebras together with their representations. Finally, we define suitable cohomology for weighted Rota-Baxter Jacobi-Jordan algebras in low degrees.

Citations

• Cohomologies and linear deformations of relative Rota-Baxter operators on (pre-)Jacobi-Jordan algebras
• Cohomology and deformations of Jacobi-Jordan algebras
• Cohomology of weighted Rota-Baxter Lie algebras and Rota-Baxter paired operators
• Deformations and homotopy theory of Rota-Baxter algebras of any weight
• Deformations of associative Rota-Baxter operators
• Weighted infinitesimal unitary bialgebras on matrix algebras and weighted associative Yang-Baxter equations
• Jacobi-Jordan algebras
• Baxter Algebras and Shuffle Products
• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem

Related

• Cohomology of weighted Rota-Baxter Lie algebras and Rota-Baxter paired operators
• Deformations of relative Rota-Baxter operators on Hom-Jacobi-Jordan algebras
• Cohomologies and linear deformations of relative Rota-Baxter operators on (pre-)Jacobi-Jordan algebras
• Weighted relative Rota-Baxter operators on Leibniz algebras and Post-Leibniz algebra structures
• Cohomologies and deformations of weighted Rota-Baxter Lie algebras and associative algebras with derivations