Cohomology of modified λ-differential Jacobi–Jordan algebras and its applications

The purpose of the present paper is to investigate cohomology of modified λ-differential Jacobi–Jordan algebras. First, we introduce the concept and representations of modified λ-differential Jacobi–Jordan algebras. Moreover, we define a lower order cohomology theory for modified λ-differential Jacobi–Jordan algebras. As applications of the proposed cohomology theory, formal deformations of modified λ-differential Jacobi–Jordan algebras are obtained and the rigidity of a modified λ-differential Jacobi–Jordan algebra is characterized by the vanishing of the second cohomology group. Also, abelian extensions of modified λ-differential Jacobi–Jordan algebras are classified by second-order cohomology. Furthermore, we study T*-extensions of modified λ-differential Jacobi–Jordan algebras.