Algebra of higher antibrackets

Беринг, Клаус; Damgaard, Poul H.; Alfaro, Jorge

doi:10.1016/0550-3213(96)00401-4

Cited by 44 publications

(74 citation statements)

References 34 publications

(81 reference statements)

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“…An alternative proof of the above theorem can be given using the results of [2], where it is (implicitly) proved that the series of higher Koszul brackets gives a morphism of graded Lie algebras and then commutes with adjoint actions; this is essentially the argument used in [7]. …”

Section: Proof It Is Immediate To Check That In D(a[2k]) One Hasmentioning

confidence: 99%

Formality of Koszul brackets and deformations of holomorphic Poisson manifolds

Fiorenza

Manetti

2012

Homology, Homotopy and Applications

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We show that if a generator of a differential Gerstenhaber algebra satisfies certain Cartan-type identities, then the corresponding Lie bracket is formal. Geometric examples include the shifted de Rham complex of a Poisson manifold and the subcomplex of differential forms on a symplectic manifold vanishing on a Lagrangian submanifold, endowed with the Koszul bracket. As a corollary we generalize a recent result by Hitchin on deformations of holomorphic Poisson manifolds.Dedicated to the memory of J.-L. Loday.

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Section: Proof It Is Immediate To Check That In D(a[2k]) One Hasmentioning

confidence: 99%

Formality of Koszul brackets and deformations of holomorphic Poisson manifolds

Fiorenza

Manetti

2012

Homology, Homotopy and Applications

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“…We denote a set of local coordinates on ΠT * X by ({u I }, {χ I }) carrying the ghost number U = ({0}, {1}). 10 Thus the space A of all fields is the space of all maps above. The odd symplectic form ω (2.31) on A is the unique extension of the odd symplectic form ω = du I dχ I with degree U = 1 on ΠT * X to A.…”

Section: Bv Quantizationmentioning

confidence: 99%

“…Akman [1] (see also [10]), motivated by VOSA and generalizing Koszul, introduced the concept of higher order differential operators on a general superalgebra. Using such a differential operator, say D, he considered the following recursive definition of higher brackets, , c),…”

Section: The First Approximationmentioning

confidence: 99%

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TOPOLOGICAL OPEN P-BRANES

Park

2001

Symplectic Geometry and Mirror Symmetry

100

155

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By exploiting the BV quantization of topological bosonic open membrane, we argue that flat 3-form C-field leads to deformations of the algebras of multi-vectors on the Dirichlet-brane world-volume as 2-algebras. This would shed some new light on geometry of M-theory 5-brane and associated decoupled theories. We show that, in general, topological open p-brane has a structure of (p + 1)-algebra in the bulk, while a structure of p-algebra in the boundary. The bulk/boundary correspondences are exactly as of the generalized Deligne conjecture (a theorem of Kontsevich) in the algebraic world of p-algebras. It also imply that the algebras of quantum observables of (p − 1)-brane are "close to" the algebras of its classical observables as p-algebras. 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 topological strings and conjecture that the homological mirror symmetry has further generalizations to the categories of p-algebras.

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“…0 , and therefore we can relate the sphere surface states as follows 11) where the Fock space label (1) is attached to the puncture at z = 0, the label (2) is attached to the puncture at w = 0, and the label (1) is attached to the special puncture.…”

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confidence: 99%

New moduli spaces from string background independence consistency conditions

Zwiebach

1996

Nuclear Physics B

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In string field theory an infinitesimal background deformation is implemented as a canonical transformation whose hamiltonian function is defined by moduli spaces of punctured Riemann surfaces having one special puncture. We show that the consistency conditions associated to the commutator of two deformations are implemented by virtue of the existence of moduli spaces of punctured surfaces with two special punctures. The spaces are antisymmetric under the exchange of the special punctures, and satisfy recursion relations relating them to moduli spaces with one special puncture and to string vertices. We develop the theory of moduli spaces of surfaces with arbitrary number of special punctures and indicate their relevance to the construction of a string field theory that makes no reference to a conformal background. Our results also imply a partial antibracket cohomology theorem for the string action.

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Algebra of higher antibrackets

Cited by 44 publications

References 34 publications

Formality of Koszul brackets and deformations of holomorphic Poisson manifolds

Formality of Koszul brackets and deformations of holomorphic Poisson manifolds

TOPOLOGICAL OPEN P-BRANES

New moduli spaces from string background independence consistency conditions

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