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Quantum Groups
TLDR
In this paper, the authors introduce the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions and present the quantum groups attached to SL2 as well as the basic concepts of the Hopf algebras.Abstract:
Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups attached to SL2 as well as the basic concepts of the theory of Hopf algebras. Coverage also focuses on Hopf algebras that produce solutions of the Yang-Baxter equation and provides an account of Drinfeld's elegant treatment of the monodromy of the Knizhnik-Zamolodchikov equations.read more
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Fault tolerant quantum computation by anyons
TL;DR: A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer Unitary transformations can be performed by moving the excitations around each other Unitary transformation can be done by joining excitations in pairs and observing the result of fusion.
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Non-Abelian Anyons and Topological Quantum Computation
TL;DR: In this article, the authors describe the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the ''ensuremath{
u}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.
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Anyons in an exactly solved model and beyond
TL;DR: In this article, a spin-1/2 system on a honeycomb lattice is studied, where the interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength.
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Deformation Quantization of Poisson Manifolds
TL;DR: In this paper, it was shown that every finite-dimensional Poisson manifold X admits a canonical deformation quantization, and that the set of equivalence classes of associative algebras close to the algebra of functions on X is in one-to-one correspondence with the class of Poisson structures on X modulo diffeomorphisms.
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Deformation quantization of Poisson manifolds, I
TL;DR: In this paper, it was shown that every finite-dimensional Poisson manifold X admits a canonical deformation quantization, which can be interpreted as correlators in topological open string theory.