Abstract

We discuss general properties of A∞-algebras and their applications to the theory of open strings. The properties of cyclicity for A∞-algebras are examined in detail. We prove the decomposition theorem, which is a stronger version of the minimal model theorem, for A∞algebras and cyclic A∞-algebras and discuss various consequences of it. In particular it is applied to classical open string field theories and it is shown that all classical open string field theories on a fixed conformal background are cyclic A∞-isomorphic to each other. The same results hold for classical closed string field theories, whose algebraic structure is governed by cyclic L∞-algebras. Contents 1 Introduction and Summary 2 1.1 A∞-space and A∞-algebras.............................. 2 1.2 A∞-structure and classical open string field theory................. 6 1.3 Dual description; formal noncommutative supermanifold.............. 13

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