On the cohomology of Banach A∞-module over admissible Banach A∞-algebra

Abstract

In this paper we are concerned with Banach A 1 -module M over admissible Banach A 1 -algebra A. We give some properties of admissible modules and algebras. We study the cohomology of the complex C 1 (A, M). We show that the vanishing of cohomology of this complex in certain dimensions implies to the existence of the A 1 -module structure.

On the perturbation of differential Banach algebra

“…In [8] simernov and others introduced the conception of Banch A ∞ -algebra and related cohomology groups. The second author have studied some classes of Banch A ∞ -algebras in [1]. In the present work we define and study the perturbation of Banach D ∞ -algebra and some its homotopy invariant property (SDR-case).…”