Representations of weighted Rota-Baxter Jacobi-Jordan algebras

TL;DR

This paper explores the structure and representations of weighted Rota-Baxter Jacobi-Jordan algebras, introduces related paired operators, and develops a cohomology theory for these algebras.

Contribution

It introduces the concept of weighted Rota-Baxter Jacobi-Jordan algebras, their representations, and a cohomology framework, advancing the theoretical understanding of these algebraic structures.

Findings

Defined weighted Rota-Baxter Jacobi-Jordan algebras

Established representations for these algebras

Developed a cohomology theory in low degrees

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.