The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
John Francis - One of the best experts on this subject based on the ideXlab platform.
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Poincaré/Koszul Duality
Communications in Mathematical Physics, 2019Co-Authors: David Ayala, John FrancisAbstract:We prove a Duality for factorization homology which generalizes both usual Poincaré Duality for manifolds and Koszul Duality for $${\mathcal{E}_n}$$ E n -algebras. The Duality has application to the Hochschild homology of associative algebras and enveloping algebras of Lie algebras. We interpret our result at the level of topological quantum field theory.
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chiral koszul Duality
Selecta Mathematica-new Series, 2012Co-Authors: John Francis, Dennis GaitsgoryAbstract:We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld (American Mathematical Society Colloquium Publications, 51. American Mathematical Society, Providence, RI, 2004), to higher-dimensional varieties. This extension entails the development of the homotopy theory of chiral and factorization structures, in a sense analogous to Quillen’s homotopy theory of differential graded Lie algebras. We prove the equivalence of higher-dimensional chiral and factorization algebras by embedding factorization algebras into a larger category of chiral commutative coalgebras, then realizing this interrelation as a chiral form of Koszul Duality. We apply these techniques to rederive some fundamental results of Beilinson and Drinfeld (American Mathematical Society Colloquium Publications, 51. American Mathematical Society, Providence, RI, 2004) on chiral enveloping algebras of \({\star}\) -Lie algebras.
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chiral koszul Duality
arXiv: Algebraic Geometry, 2011Co-Authors: John Francis, Dennis GaitsgoryAbstract:We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld in \cite{bd}, to higher-dimensional varieties. This extension entails the development of the homotopy theory of chiral and factorization structures, in a sense analogous to Quillen's homotopy theory of differential graded Lie algebras. We prove the equivalence of higher-dimensional chiral and factorization algebras by embedding factorization algebras into a larger category of chiral commutative coalgebras, then realizing this interrelation as a chiral form of Koszul Duality. We apply these techniques to rederive some fundamental results of \cite{bd} on chiral enveloping algebras of $\star$-Lie algebras.
Gui-lu Long - One of the best experts on this subject based on the ideXlab platform.
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Duality Quantum Information and Duality Quantum Communication
2011Co-Authors: W. Y. Wang, C. Wang, S. Y. Song, Gui-lu LongAbstract:Quantum mechanical systems exhibit particle wave Duality property. This Duality property has been exploited for information processing. A Duality quantum computer is a quantum computer on the move and passing through a multi‐slits. It offers quantum wave divider and quantum wave combiner operations in addition to those allowed in an ordinary quantum computer. It has been shown that all linear bounded operators can be realized in a Duality quantum computer, and a Duality quantum computer with n qubits and d‐slits can be realized in an ordinary quantum computer with n qubits and a qudit in the so‐called Duality quantum computing mode. The quantum particle‐wave Duality can be used in providing secure communication. In this paper, we will review Duality quantum computing and Duality quantum key distribution.
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Duality Quantum Computing and Duality Quantum Information Processing
International Journal of Theoretical Physics, 2010Co-Authors: Gui-lu LongAbstract:Quantum mechanical systems exhibit wave-particle Duality property. This Duality property has been exploited for information processing. A Duality quantum computer is a quantum computer on the move and passing through a multi-slits. It offers quantum wave divider and quantum wave combiner operations in addition to those allowed in an ordinary quantum computer. It has been shown that all linear bounded operators can be realized in a Duality quantum computer, and a Duality quantum computer with n qubits and d-slits can be realized in an ordinary quantum computer with n qubits and a qudit in the so-called Duality quantum computing mode. In this article, the main structure of Duality quantum computing, their mathematical description and applications are reviewed.
Ilya Bakhmatov - One of the best experts on this subject based on the ideXlab platform.
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Fermionic T-Duality in massive type IIA supergravity on $$AdS_{10-k} \times M_k$$ A
The European Physical Journal C, 2016Co-Authors: Ilya BakhmatovAbstract:Fermionic T-Duality transformation is studied for supersymmetric solutions of massive type IIA supergravity with the metric $$AdS_{10-k} \times M_k$$ A d S 10 - k × M k for $$k=3$$ k = 3 and 5. We derive the Killing spinors of these backgrounds and use them as input for the fermionic T-Duality transformation. The resulting dual solutions form a large family of supersymmetric deformations of the original solutions by complex valued RR fluxes. We observe that the Romans mass parameter does not change under fermionic T-duaity, and prove its invariance in the $$k=3$$ k = 3 case.
Dennis Gaitsgory - One of the best experts on this subject based on the ideXlab platform.
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chiral koszul Duality
Selecta Mathematica-new Series, 2012Co-Authors: John Francis, Dennis GaitsgoryAbstract:We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld (American Mathematical Society Colloquium Publications, 51. American Mathematical Society, Providence, RI, 2004), to higher-dimensional varieties. This extension entails the development of the homotopy theory of chiral and factorization structures, in a sense analogous to Quillen’s homotopy theory of differential graded Lie algebras. We prove the equivalence of higher-dimensional chiral and factorization algebras by embedding factorization algebras into a larger category of chiral commutative coalgebras, then realizing this interrelation as a chiral form of Koszul Duality. We apply these techniques to rederive some fundamental results of Beilinson and Drinfeld (American Mathematical Society Colloquium Publications, 51. American Mathematical Society, Providence, RI, 2004) on chiral enveloping algebras of \({\star}\) -Lie algebras.
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chiral koszul Duality
arXiv: Algebraic Geometry, 2011Co-Authors: John Francis, Dennis GaitsgoryAbstract:We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld in \cite{bd}, to higher-dimensional varieties. This extension entails the development of the homotopy theory of chiral and factorization structures, in a sense analogous to Quillen's homotopy theory of differential graded Lie algebras. We prove the equivalence of higher-dimensional chiral and factorization algebras by embedding factorization algebras into a larger category of chiral commutative coalgebras, then realizing this interrelation as a chiral form of Koszul Duality. We apply these techniques to rederive some fundamental results of \cite{bd} on chiral enveloping algebras of $\star$-Lie algebras.
David Ayala - One of the best experts on this subject based on the ideXlab platform.
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Poincaré/Koszul Duality
Communications in Mathematical Physics, 2019Co-Authors: David Ayala, John FrancisAbstract:We prove a Duality for factorization homology which generalizes both usual Poincaré Duality for manifolds and Koszul Duality for $${\mathcal{E}_n}$$ E n -algebras. The Duality has application to the Hochschild homology of associative algebras and enveloping algebras of Lie algebras. We interpret our result at the level of topological quantum field theory.
