Noncommutative homotopy algebras associated with open strings

We discuss general properties of A(infinity)-algebras and their applications to the theory of open strings. The properties of cyclicity for A(infinity)-algebras are examined in detail. We prove the decomposition theorem, which is a stronger version of the minimal model theorem, for A(infinity)-algebras and cyclic A(infinity)-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(infinity)-isomorphic to each other. The same results hold for classical closed string field theories, whose algebraic structure is governed by cyclic L-infinity-algebras.