Perturbation Differential A-Infinity Algebra

In the present paper, we investigate and introduce the perturbation of dA∞-algebra and the homotopy property (SDR-case). We also verify the homotopy theory of dA∞-algebras and A∞- differential module. In addition, We construct a property of homotopy invariant property of A∞-differential algebras

Differential Graded Algebras and Derived E∞-Algebras

In this paper, we introduce the derived E-infinity and the homology of differential graded algebra and seen as an E- infinity algebra.We display two hypotheses of the homology theory of differential graded algebra A over commutative ground ring k. Furthermore, exhibit that it is the minimal derived E∞-algebra. Finally, we give satisfying fitting relations in the class E-infinity algebra

Dihedral Cohomology of an Infinity Algebras

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