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32
Noncommutative homotopy algebras associated with open strings
 REV. MATH. PHYS
, 2003
"... 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 a ..."
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Cited by 28 (5 self)
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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.
Openclosed homotopy algebra in mathematical physics
 J. Math. Phys
"... In this paper we discuss various aspects of openclosed homotopy algebras (OCHAs) presented in our previous paper, inspired by Zwiebach’s openclosed string field theory, but that first paper concentrated on the mathematical aspects. Here we show how an OCHA is obtained by extracting the tree part o ..."
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Cited by 17 (2 self)
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In this paper we discuss various aspects of openclosed homotopy algebras (OCHAs) presented in our previous paper, inspired by Zwiebach’s openclosed string field theory, but that first paper concentrated on the mathematical aspects. Here we show how an OCHA is obtained by extracting the tree part of Zwiebach’s quantum openclosed string field theory. We clarify the explicit relation of an OCHA with Kontsevich’s deformation quantization and with the Bmodels of homological mirror symmetry. An explicit form of the minimal model for an OCHA is given as well as its relation to the perturbative expansion of openclosed string field theory. We show that our openclosed homotopy algebra gives us a general scheme for deformation of open string structures (A∞algebras) by closed strings (L∞algebras).
Closed/open string diagrammatics
 Nucl. Phys. B
"... Abstract. We introduce a combinatorial model based on measured foliations in surfaces which captures the phenomenology of open/closed string interactions. All of the predicted equations of string theory are derived in this model, and new equations can be discovered as well. In particular, several ne ..."
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Cited by 8 (2 self)
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Abstract. We introduce a combinatorial model based on measured foliations in surfaces which captures the phenomenology of open/closed string interactions. All of the predicted equations of string theory are derived in this model, and new equations can be discovered as well. In particular, several new equations together with known transformations generate the combinatorial version of open/closed duality. On the topological and chain levels, the algebraic structure discovered is new, but it specializes to a modular bioperad on the level of homology.
Categories of holomorphic line bundles on higher dimensional noncommutative complex tori
, 2005
"... ..."
AN ∞algebras
 In preparation
"... We study higher depth algebras. We introduce several examples of such structures starting from the notion of Ndifferential graded algebras and build up to the concept of A N ∞algebras. 1 ..."
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Cited by 3 (3 self)
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We study higher depth algebras. We introduce several examples of such structures starting from the notion of Ndifferential graded algebras and build up to the concept of A N ∞algebras. 1