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96
DBranes on CalabiYau Manifolds and Superpotentials
, 2002
"... We show how to compute terms in an expansion of the worldvolume superpotential for fairly general Dbranes on the quintic CalabiYau using linear sigma model techniques, and show in examples that this superpotential captures the geometry and obstruction theory of bundles and sheaves on this Calabi ..."
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Cited by 24 (4 self)
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We show how to compute terms in an expansion of the worldvolume superpotential for fairly general Dbranes on the quintic CalabiYau using linear sigma model techniques, and show in examples that this superpotential captures the geometry and obstruction theory of bundles and sheaves on this CalabiYau.
Regular algebras of dimension 4 and their A∞Extalgebras
 Duke Math. J
"... ABSTRACT. We construct four families of ArtinSchelter regular algebras of global dimension four. Under some generic conditions, this is a complete list of ArtinSchelter regular algebras of global dimension four that are generated by two elements of degree 1. These algebras are also strongly noethe ..."
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Cited by 22 (10 self)
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ABSTRACT. We construct four families of ArtinSchelter regular algebras of global dimension four. Under some generic conditions, this is a complete list of ArtinSchelter regular algebras of global dimension four that are generated by two elements of degree 1. These algebras are also strongly noetherian, Auslander regular and CohenMacaulay. One of the main tools is Keller’s highermultiplication theorem on A∞Extalgebras.
WHEELED PROPS, GRAPH COMPLEXES AND THE MASTER EQUATION
, 2007
"... We introduce and study wheeled PROPs, an extension of the theory of PROPs which can treat traces and, in particular, solutions to the master equations which involve divergence operators. We construct a dg free wheeled PROP whose representations are in onetoone correspondence with formal germs of ..."
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Cited by 18 (6 self)
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We introduce and study wheeled PROPs, an extension of the theory of PROPs which can treat traces and, in particular, solutions to the master equations which involve divergence operators. We construct a dg free wheeled PROP whose representations are in onetoone correspondence with formal germs of SPmanifolds, key geometric objects in the theory of BatalinVilkovisky quantization. We also construct minimal wheeled resolutions of classical operads Com and As s as rather nonobvious extensions of Com ∞ and As s∞, involving, e.g., a mysterious mixture of associahedra with cyclohedra. Finally, we apply the above results to a computation of cohomology of a directed version of Kontsevich’s complex of ribbon graphs.
A∞structures on an elliptic curve
 in Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds, 275–295. AMS and International
, 2001
"... Let E be an elliptic curve over a field k. Let us denote by Vect(E) the category of algebraic vector bundles on E, where as space of morphisms from V1 to V2 we take the graded space Hom(V1, V2)⊕Ext 1 (V1, V2) with the natural composition law. In this paper we study extensions of this (strictly assoc ..."
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Cited by 17 (1 self)
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Let E be an elliptic curve over a field k. Let us denote by Vect(E) the category of algebraic vector bundles on E, where as space of morphisms from V1 to V2 we take the graded space Hom(V1, V2)⊕Ext 1 (V1, V2) with the natural composition law. In this paper we study extensions of this (strictly associative) composition to A∞structures on Vect(E) (see section 1 for the definition). The motivation comes from
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).
Ainfinity structure on Extalgebras
, 2006
"... Abstract. Let A be a connected graded algebra and let E denote its Extalgebra i Exti A (kA, kA). There is a natural A∞structure on E, and we prove that this structure is mainly determined by the relations of A. In particular, the coefficients of the A∞products mn restricted to the tensor powers of ..."
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Cited by 17 (1 self)
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Abstract. Let A be a connected graded algebra and let E denote its Extalgebra i Exti A (kA, kA). There is a natural A∞structure on E, and we prove that this structure is mainly determined by the relations of A. In particular, the coefficients of the A∞products mn restricted to the tensor powers of Ext1 A (kA, kA) give the coefficients of the relations of A. We also relate the mn’s to Massey products.
Dbrane superpotentials in CalabiYau orientifolds
, 2006
"... We develop computational tools for the treelevel superpotential of Bbranes in CalabiYau orientifolds. Our method is based on a systematic implementation of the orientifold projection in the geometric approach of Aspinwall and Katz. In the process we lay down ..."
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Cited by 10 (2 self)
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We develop computational tools for the treelevel superpotential of Bbranes in CalabiYau orientifolds. Our method is based on a systematic implementation of the orientifold projection in the geometric approach of Aspinwall and Katz. In the process we lay down
AInfinity Algebras in Representation Theory
, 2001
"... We give a brief introduction to A1algebras and show three contexts in which they appear in representation theory: the study of Yoneda algebras and Koszulity, the description of categories of ltered modules and the description of triangulated categories. Contents 1. Denitions, the bar construction, ..."
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Cited by 8 (0 self)
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We give a brief introduction to A1algebras and show three contexts in which they appear in representation theory: the study of Yoneda algebras and Koszulity, the description of categories of ltered modules and the description of triangulated categories. Contents 1. Denitions, the bar construction, the minimality theorem 1 2. Yoneda algebras, Koszulity and ltered modules 5 3. Description of triangulated categories 8 References 10 1. Definitions, the bar construction, the minimality theorem 1.1. Ainnity algebras and morphisms. We refer to [11] for a list of references and a topological motivation for the following denition: Let k be a eld. An A1  algebra over k is a Zgraded vector space A = M p2Z A p endowed with graded maps (=homogeneous klinear maps) mn : A