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

Abstract

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

Keywords

• Banach A∞-module–admissible Banach A∞-algebra
• Cohomology group