Results 1  10
of
19
Topological Open pBranes
, 2000
"... By exploiting the BV quantization of topological bosonic open membrane, we argue that flat 3form Cfield leads to deformations of the algebras of multivectors on the Dirichletbrane worldvolume as 2algebras. This would shed some new light on geometry of Mtheory 5brane and associated decoupled ..."
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Cited by 36 (1 self)
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By exploiting the BV quantization of topological bosonic open membrane, we argue that flat 3form Cfield leads to deformations of the algebras of multivectors on the Dirichletbrane worldvolume as 2algebras. This would shed some new light on geometry of Mtheory 5brane and associated decoupled theories. We show that, in general, topological open pbrane has a structure of (p + 1)algebra in the bulk, while a structure of palgebra in the boundary. The bulk/boundary correspondences are exactly as of the generalized Deligne conjecture (a theorem of Kontsevich) in the algebraic world of palgebras. It also imply that the algebras of quantum observables of (p − 1)brane are “close to ” the algebras of its classical observables as palgebras. We interpret above as deformation quantization of (p − 1)brane, generalizing the p = 1 case. We argue that there is such quantization based on the direct relation between BV master equation and Ward identity of the bulk topological theory. The path integral of the theory will lead to the explicit formula. We also discuss some applications to
On the structure of cofree Hopf algebras
 J. reine angew. Math
"... Abstract. We prove an analogue of the PoincaréBirkhoffWitt theorem and of the CartierMilnorMoore theorem for noncocommutative Hopf algebras. The primitive part of a cofree Hopf algebra is a nondifferential B∞algebra. We construct a universal enveloping functor U2 from nondifferential B∞algebr ..."
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Cited by 36 (4 self)
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Abstract. We prove an analogue of the PoincaréBirkhoffWitt theorem and of the CartierMilnorMoore theorem for noncocommutative Hopf algebras. The primitive part of a cofree Hopf algebra is a nondifferential B∞algebra. We construct a universal enveloping functor U2 from nondifferential B∞algebras to 2associative algebras, i.e. algebras equipped with two associative operations. We show that any cofree Hopf algebra H is of the form U2(Prim H). We take advantage of the description of the free 2asalgebra in terms of planar trees to unravel the operad associated to nondifferential B∞algebras.
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 32 (2 self)
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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 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 with ∆ replaced by an arbitrary odd derivation. We discuss applications and links with other constructions.
Generalized bialgebras and triples of operads
, 2006
"... Key words and phrases. Bialgebra, generalized bialgebra, Hopf algebra, CartierMilnorMoore, PoincaréBirkhoffWitt, operad, prop, triple of operads, primitive part, dendriform algebra, duplicial algebra, preLie ..."
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Cited by 16 (5 self)
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Key words and phrases. Bialgebra, generalized bialgebra, Hopf algebra, CartierMilnorMoore, PoincaréBirkhoffWitt, operad, prop, triple of operads, primitive part, dendriform algebra, duplicial algebra, preLie
On Quantization of Quadratic Poisson Structures
 Comm. in Math. Phys
"... Abstract: Any classical rmatrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel’d [Dr], [Gr]. We exhibit in this article an example of quadratic Pois ..."
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Cited by 10 (4 self)
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Abstract: Any classical rmatrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel’d [Dr], [Gr]. We exhibit in this article an example of quadratic Poisson structure which does not arise this way. I.
ON DERIVATION DEVIATIONS IN AN ABSTRACT PREOPERAD
, 2001
"... Abstract. We consider basic algebraic constructions associated with an abstract preoperad, such as a ⌣algebra, total composition •, precoboundary operator δ and tribraces {·, ·, ·}. A derivation deviation of the precoboundary operator over the tribraces is calculated in terms of the ⌣multiplicat ..."
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Cited by 9 (6 self)
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Abstract. We consider basic algebraic constructions associated with an abstract preoperad, such as a ⌣algebra, total composition •, precoboundary operator δ and tribraces {·, ·, ·}. A derivation deviation of the precoboundary operator over the tribraces is calculated in terms of the ⌣multiplication and total composition. Classification (MSC2000). 18D50. Key words. Comp(osition), (pre)operad, Gerstenhaber theory, cup,
A Hopf operad of forests of binary trees and related finitedimensional algebras
, 2002
"... The structure of a Hopf operad is defined on the vector spaces spanned by forests of leaflabeled, rooted, binary trees. An explicit formula for the coproduct and its dual product is given, using a poset on forests. 0 ..."
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Cited by 6 (6 self)
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The structure of a Hopf operad is defined on the vector spaces spanned by forests of leaflabeled, rooted, binary trees. An explicit formula for the coproduct and its dual product is given, using a poset on forests. 0
Homotopy algebras for operads
"... We present a definition of homotopy algebra for an operad, and explore its consequences. The paper should be accessible to topologists, category theorists, and anyone acquainted with operads. After a review of operads and monoidal categories, the definition of homotopy algebra is given. Specifically ..."
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Cited by 6 (1 self)
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We present a definition of homotopy algebra for an operad, and explore its consequences. The paper should be accessible to topologists, category theorists, and anyone acquainted with operads. After a review of operads and monoidal categories, the definition of homotopy algebra is given. Specifically, suppose that M is a monoidal category in which it makes sense to talk about algebras for some operad P. Then our definition says what a homotopy Palgebra in M is, provided only that some of the morphisms in M have been marked out as ‘homotopy equivalences’. The bulk of the paper consists of examples of homotopy algebras. We show that any loop space is a homotopy monoid, and, in fact, that any nfold loop space is an nfold homotopy monoid in an appropriate sense. We try to compare weakened algebraic structures such as A∞spaces, A∞algebras and nonstrict monoidal categories to our homotopy algebras, with varying degrees of success. We also prove results on ‘change of base’, e.g. that the classifying space of a homotopy monoidal category is a homotopy topological monoid. Finally, we
Cohomology operations and the Deligne conjecture
 Czechoslovak Math. J
"... Abstract. The aim of this note, which raises more questions than it answers, is to study natural operations acting on the cohomology of various types of algebras. It contains a lot of very surprising partial results and examples. ..."
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Cited by 5 (3 self)
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Abstract. The aim of this note, which raises more questions than it answers, is to study natural operations acting on the cohomology of various types of algebras. It contains a lot of very surprising partial results and examples.
What do dgcategories form
 Compositio Math
"... It is well known that categories form a 2category: 1arrows are functors and 2arrows are their natural transformations. In a similar way, dgcategories also form a 2category: 1arrows A → B are dgfunctors; given a pair of dgfunctors F,G: A → B one can define a complex of their natural transform ..."
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Cited by 4 (1 self)
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It is well known that categories form a 2category: 1arrows are functors and 2arrows are their natural transformations. In a similar way, dgcategories also form a 2category: 1arrows A → B are dgfunctors; given a pair of dgfunctors F,G: A → B one can define a complex of their natural transformations