Symplectic Forms and the Yang-Baxter Equation in Jacobi-Jordan algebras

This paper's primary objective is to expand the connection be-tween the presence of a symplectic form on a Mock-Lie algebra and the solution of the Yang-Baxter equation (YBE) into the realm of sym-plectic Jacobi-Jordan algebras. The study establishes an equivalence between the existence of an even symplectic form omega on a Mock-Lie algebra and the existence of an r-matrix of J, which is a solution r of the YBE.