Noncommutative homotopy algebras associated with open strings

Details Noncommutative homotopy algebras associated with open strings Noncommutative homotopy algebras associated with open strings

2003-06-23

arxiv.org/abs/math/0306332v2

Rev.Math.Phys.19:1-99,2007

Mathematics

Quantum Algebra

92 pages, 16 figuers; based on Ph.D thesis submitted to Graduate School of Mathematical Sciences, Univ. of Tokyo on January, 2

Scientific paper

10.1142/S0129055X07002912

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

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