Search results for "Quantum algebra"

showing 7 items of 117 documents

Topological Hopf algebras, quantum groups and deformation quantization

2003

After a presentation of the context and a brief reminder of deformation quantization, we indicate how the introduction of natural topological vector space topologies on Hopf algebras associated with Poisson Lie groups, Lie bialgebras and their doubles explains their dualities and provides a comprehensive framework. Relations with deformation quantization and applications to the deformation quantization of symmetric spaces are described

[ MATH.MATH-QA ] Mathematics [math]/Quantum Algebra [math.QA]quantum groups[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]FOS: Physical sciences[ MATH.MATH-SG ] Mathematics [math]/Symplectic Geometry [math.SG]topological vector spacesMathematical Physics (math-ph)[MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG]deformation quantizationMathematics - Symplectic GeometryHopf algebras54C40 14E20 (primary) 46E25 20C20 (secondary)[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]Mathematics::Quantum AlgebraMathematics - Quantum AlgebraFOS: Mathematics[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA]Quantum Algebra (math.QA)Symplectic Geometry (math.SG)Mathematical Physics
researchProduct

Geometrical construction of quantum groups representations

2002

We describe geometrically the classical and quantum inhomogeneous groups $G_0=(SL(2, \BbbC)\triangleright \BbbC^2)$ and $G_1=(SL(2, \BbbC)\triangleright \BbbC^2)\triangleright \BbbC$ by studying explicitly their shape algebras as a spaces of polynomial functions with a quadratic relations.

[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA][ MATH.MATH-QA ] Mathematics [math]/Quantum Algebra [math.QA]Mathematics - Quantum AlgebraFOS: Mathematics[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA]Quantum Algebra (math.QA)
researchProduct

Kontsevich and Takhtajan construction of star product on the Poisson Lie group GL(2)

2001

Comparing the star product defined by Takhtajan on the Poisson-Lie group GL(2) and any star product calculated from the Kontsevich's graphs (any ''K-star product'') on the same group, we show, by direct computation, that the Takhtajan star product on GL(2) can't be written as a K-star product.

[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA][ MATH.MATH-QA ] Mathematics [math]/Quantum Algebra [math.QA][PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph][ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]FOS: Physical sciencesMathematical Physics (math-ph)Astrophysics::Cosmology and Extragalactic Astrophysics[PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph][MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]Mathematics::Quantum AlgebraMathematics - Quantum AlgebraFOS: Mathematics[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA]Quantum Algebra (math.QA)Astrophysics::Solar and Stellar Astrophysics[ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph]Astrophysics::Earth and Planetary Astrophysics[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]Astrophysics::Galaxy AstrophysicsMathematical Physics
researchProduct

A possible quantic motivation of the structure of quantum group: continuation

2012

Motivated by Quantum Mechanics considerations, we expose some cross product constructions on a groupoid structure. Furthermore, critical remarks are made on some basic formal aspects of the Hopf algebra structure.

[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA][PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]groupoid semigroupoid cross product quantum group[MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA][MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA][MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA][PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph]ComputingMilieux_MISCELLANEOUS
researchProduct

Comparison of frictional resistance between passive self-ligating brackets and slide-type low-friction ligature brackets during the alignment and lev…

2019

Background To compare the frictional resistance between passive self-ligating brackets and conventional brackets with low-friction ligature under bracket/archwire and root/bone interface during dental alignment and leveling. Material and methods A tridimensional model of the maxilla and teeth of a patient treated with conventional brackets, and slide ligatures was generated employing the SolidWorks modeling software. SmartClip self-ligating brackets and Logic Line conventional brackets were assembled with slide low-friction ligatures, utilizing archwires with different diameters and alloys used for the alignment and leveling stage. Friction caused during the bracket/archwire interface and s…

musculoskeletal diseasesModeling softwareMaterials sciencemedicine.medical_treatmentPhysics::Medical PhysicsOrthodonticsLow frictionStress (mechanics)03 medical and health sciences0302 clinical medicineMathematics::Quantum Algebramedicine030223 otorhinolaryngologyLigatureGeneral DentistryMathematics::Symplectic GeometryOrthodontic FrictionOrthodonticsOrthodontic wireintegumentary systemResearchBracket030206 dentistry:CIENCIAS MÉDICAS [UNESCO]musculoskeletal systemNonlinear Sciences::Exactly Solvable and Integrable SystemsUNESCO::CIENCIAS MÉDICASFrictional resistancehuman activitiesJournal of Clinical and Experimental Dentistry
researchProduct

Jeu de Taquin and Diamond Cone for so(2n+1, C)

2020

International audience; The diamond cone is a combinatorial description for a basis of a natural indecomposable n-module, where n is the nilpotent factor of a complex semisimple Lie algebra g. After N. J. Wildberger who introduced this notion, this description was achieved for g = sl(n) , the rank 2 semisimple Lie algebras and g = sp (2n).In this work, we generalize these constructions to the Lie algebra g = so(2n + 1). The orthogonal semistandard Young tableaux were defined by M. Kashiwara and T. Nakashima, they index a basis for the shape algebra of so(2n + 1). Defining the notion of orthogonal quasistandard Young tableaux, we prove that these tableaux describe a basis for a quotient of t…

quasistandard Young tableauMathematics::Quantum AlgebraShape algebrajeu de taquinMSC: 20G05 05A15 17B10[MATH] Mathematics [math][MATH]Mathematics [math]Mathematics::Representation Theorysemistandard Young tableau
researchProduct

Deformation Quantization in White Noise Analysis

2007

We define and present an example of a deformation quantization product on a Hida space of test functions endowed with a Wick product.

white noise analysisMoyal productQuantization (signal processing)lcsh:MathematicsMathematics::Number TheoryMathematical analysisFOS: Physical sciencesWhite noiseMathematical Physics (math-ph)lcsh:QA1-939Mathematics - Quantum AlgebraFOS: MathematicsMoyal productQuantum Algebra (math.QA)Geometry and TopologyWick productAnalysisMathematical PhysicsMathematicsMathematical physics
researchProduct