Search results for "16W30"

showing 3 items of 3 documents

Quantization of Poisson Lie Groups and Applications

1996

LetG be a connected Poisson-Lie group. We discuss aspects of the question of Drinfel'd:can G be quantized? and give some answers. WhenG is semisimple (a case where the answer isyes), we introduce quantizable Poisson subalgebras ofC ∞(G), related to harmonic analysis onG; they are a generalization of F.R.T. models of quantum groups, and provide new examples of quantized Poisson algebras.

58B30Pure mathematicsGeneralizationPoisson distribution01 natural sciencesHarmonic analysissymbols.namesakeQuantization (physics)58F060103 physical sciences0101 mathematicsQuantumMathematical PhysicsComputingMilieux_MISCELLANEOUSMathematicsPoisson algebraDiscrete mathematics[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]Group (mathematics)010102 general mathematicsLie groupStatistical and Nonlinear Physics81S1017B37[ MATH.MATH-RT ] Mathematics [math]/Representation Theory [math.RT]symbols010307 mathematical physics16W30
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The hidden group structure of quantum groups: strong duality, rigidity and preferred deformations

1994

A notion of well-behaved Hopf algebra is introduced; reflexivity (for strong duality) between Hopf algebras of Drinfeld-type and their duals, algebras of coefficients of compact semi-simple groups, is proved. A hidden classical group structure is clearly indicated for all generic models of quantum groups. Moyal-product-like deformations are naturally found for all FRT-models on coefficients andC∞-functions. Strong rigidity (H bi 2 ={0}) under deformations in the category of bialgebras is proved and consequences are deduced.

Classical groupPure mathematicsQuantum groupDeformation theoryLie groupStatistical and Nonlinear PhysicsHopf algebra17B37Algebra81R50Compact groupMathematics::Quantum AlgebraStrong dualityDual polyhedron16W30Mathematical PhysicsMathematics
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Multiple Noncommutative Tori and Hopf Algebras

2001

We derive the Kac-Paljutkin finite-dimensional Hopf algebras as finite fibrations of the quantum double torus and generalize the construction for quantum multiple tori.

PhysicsPure mathematicsAlgebra and Number TheoryFOS: Physical sciencesTorusMathematics - Rings and AlgebrasMathematical Physics (math-ph)Hopf algebraNoncommutative geometry16W30 57T05Rings and Algebras (math.RA)Mathematics::Quantum AlgebraMathematics - Quantum AlgebraFOS: MathematicsQuantum Algebra (math.QA)Mathematics::Symplectic GeometryQuantumMathematical PhysicsCommunications in Algebra
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