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135
Noncommutative differential calculus, homotopy . . .
, 2000
"... We define a notion of a strong homotopy BV algebra and apply it to deformation theory problems. Formality conjectures for Hochschild cochains are formulated. We prove several results supporting these conjectures. ..."
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Cited by 57 (1 self)
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We define a notion of a strong homotopy BV algebra and apply it to deformation theory problems. Formality conjectures for Hochschild cochains are formulated. We prove several results supporting these conjectures.
Chicken or egg? A hierarchy of . . .
, 2008
"... We start by clarifying and extending the multibraces notation which economically describes substitutions of multilinear maps and tensor products of vectors. We give definitions and examples of homotopy algebras, strongly homotopy Gerstenhaber and Gerstenhaber bracket algebras, and strongly homotopy ..."
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been proven by Kimura, Voronov, and Zuckerman in 1996 (later amended by Voronov). The contention that this is the fundamental structure on a TVOA is substantiated by providing an annotated dictionary of strongly homotopy BV algebra maps and
Strong homotopy algebras of a Kähler manifold
 math.AG/9809172, Int. Math. Res. Notices
, 1999
"... It is shown that any compact Kähler manifold M gives canonically rise to two strongly homotopy algebras, the first one being associated with the Hodge theory of the de Rham complex and the second one with the Hodge theory of the Dolbeault complex. In these algebras the product of two harmonic differ ..."
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Cited by 96 (9 self)
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It is shown that any compact Kähler manifold M gives canonically rise to two strongly homotopy algebras, the first one being associated with the Hodge theory of the de Rham complex and the second one with the Hodge theory of the Dolbeault complex. In these algebras the product of two harmonic
Courant algebroids and strongly homotopy Lie algebras
 Lett. Math. Phys
, 1998
"... Abstract. Courant algebroids are structures which include as examples the doubles of Lie bialgebras and the bundle TM ⊕ T ∗ M with the bracket introduced by T. Courant for the study of Dirac structures. Within the category of Courant algebroids one can construct the doubles of Lie bialgebroids, the ..."
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Cited by 68 (5 self)
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, the infinitesimal objects for Poisson groupoids. We show that Courant algebroids can be considered as strongly homotopy Lie algebras. 1.
Homotopy DG algebras induce homotopy BV algebras”, preprint
"... Abstract Let T A denote the space underlying the tensor algebra of a vector space A. In this short note, we show that if A is a differential graded algebra, then T A is a differential BatalinVilkovisky algebra. Moreover, if A is an A ∞ algebra, then T A is a commutative BV ∞ algebra. ..."
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Cited by 4 (1 self)
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Abstract Let T A denote the space underlying the tensor algebra of a vector space A. In this short note, we show that if A is a differential graded algebra, then T A is a differential BatalinVilkovisky algebra. Moreover, if A is an A ∞ algebra, then T A is a commutative BV ∞ algebra.
Homotopy Batalin–Vilkovisky algebras
"... This paper provides an explicit cofibrant resolution of the operad encoding BatalinVilkovisky algebras. Thus it defines the notion of homotopy BatalinVilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads ..."
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Cited by 34 (4 self)
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resolution enables us to describe the deformation theory and homotopy theory of BValgebras and of homotopy BValgebras. We show that any topological conformal field theory carries a homotopy BValgebra structure which lifts the BValgebra structure on homology. The same result is proved for the singular
THE HOMOTOPY THEORY OF STRONG HOMOTOPY ALGEBRAS AND BIALGEBRAS
, 2009
"... Lada introduced strong homotopy algebras to describe the structures on a deformation retract of an algebra in topological spaces. However, there is no satisfactory general definition of a morphism of strong homotopy (s.h.) algebras. Given a monad ⊤ on a simplicial category C, we instead show how s ..."
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Cited by 4 (2 self)
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Lada introduced strong homotopy algebras to describe the structures on a deformation retract of an algebra in topological spaces. However, there is no satisfactory general definition of a morphism of strong homotopy (s.h.) algebras. Given a monad ⊤ on a simplicial category C, we instead show how
Higher derived brackets and homotopy algebras
"... Abstract. We give a construction of homotopy algebras based on “higher derived brackets”. More precisely, the data include a Lie superalgebra with a projector on an Abelian subalgebra satisfying a certain axiom, and an odd element ∆. Given this, we introduce an infinite sequence of higher brackets o ..."
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Cited by 77 (5 self)
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on the image of the projector, and explicitly calculate their Jacobiators in terms of ∆ 2. This allows to control higher Jacobi identities in terms of the “order ” of ∆ 2. Examples include Stasheff’s strongly homotopy Lie algebras and variants of homotopy Batalin–Vilkovisky algebras. There is a generalization
Homotopy BValgebra structure on the double cobar construction
"... France. We show that the double cobar construction, Ω2C∗(X), of a simplicial set X is a homotopy BValgebra if X is a double suspension, or if X is 2reduced and the coefficient ring contains the field of rational numbers Q. Indeed, the ConnesMoscovici operator defines the desired homotopy BValgeb ..."
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France. We show that the double cobar construction, Ω2C∗(X), of a simplicial set X is a homotopy BValgebra if X is a double suspension, or if X is 2reduced and the coefficient ring contains the field of rational numbers Q. Indeed, the ConnesMoscovici operator defines the desired homotopy BValgebra
Results 1  10
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