Dihedral cohomology of an infinity algebra

In this research, the basic definitions of an operad, graded algebra, and A∞-module are introduced. The A∞-algebras and their (co)homology are studied to obtain the relations between the cyclic and dihedral (co)homology. The L∞-algebras are discussed, and the relations of the isomorphism between primitive and indecomposable elements in the L∞-algebras are presented. We demonstrate the relation between cyclic and dihedral (co)homology of L∞-algebras. Finally, the Mayer-Vietoris sequence of L∞-algebras is investigated.