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Quantum group

In mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital separable C*-algebras), and bicrossproduct…

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Overview

Intuitive meaning

Drinfeld–Jimbo type quantum groups

Compact matrix quantum groups

Bicrossproduct quantum groups

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Quantum group

Nodes83
Edges82
Triples119
Avg. degree1.98
Density0.024096
Components1

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Quantum group

Top relations

related to References · 53
Quantum group → American Mathematical Society, Australian Mathematical Society Lecture, Berlin, Bibcode, Birkhäuser, Cambridge, Cambridge University Press, CBO9780511549892, CBO9780511618505, Christian, Drinfeld, From, George, Gerhard, Graduate Texts, Grensing, International Press, Introduction, ISBN, Jagannathan
related to Intuitive meaning · 16
Quantum group → Alain Connes, Baxter, Evgeny Sklyanin, Hopf, Japanese School, Leningrad School, Leon Takhtajan, Lie, Ludwig Faddeev, More, Nicolai Reshetikhin, One, The, This, Vladimir Korepin, Yang
related to Drinfeld–Jimbo type quantum groups · 11
Quantum group → Cartan, Hopf, Kac, Let, Lie, Michio Jimbo, Moody, One, The, Uq, Vladimir Drinfeld
related to Description and classification by root-systems and Dynkin diagrams · 9
Quantum group → Andruskiewitsch, Borel, Cartan, Hopf, In, Schneider, Semisimple Lie, There, Uq
related to Bicrossproduct quantum groups · 6
Quantum group → Drinfeld-Jimbo, Lie, Mackey, The, They, Whereas
related to Compact matrix quantum groups · 6
Quantum group → By, Compact, Gelfand, Hausdorff, The, Woronowicz
related to Representation theory · 6
Quantum group → As, Hopf, Just, Kac, Moody, Uq
related to Example · 3
Quantum group → An, So SUμ, SUμ
related to General definition · 3
Quantum group → As, C0, The
related to Representations · 2
Quantum group → Furthermore, Hopf

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Important terminology

quantum group groups algebra hopf algebras representation compact weight lie module matrix also highest -algebra bicrossproduct uq displaystyle functions case

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Quantum groupis aspecial case of a noncommutative geometry.The continuous complex-valued functions on a compact Hausdorff topological space form a commutative C0.90text
the above Uqinstance ofand found a particularly well behaved base called a crystal base.Description and classification by root-systems and Dynkin diagramsThere has been considerable progress in descri…0.80text
the above Uqinstance ofDescription and classification by root-systems and Dynkin diagramsThere has been considerable progress in describing finite quotients of quantum groups0.80text
Quantum grouprelated to Bicrossproduct quantum groupsWhereas0.60section
Quantum grouprelated to Bicrossproduct quantum groupsDrinfeld-Jimbo0.60section
Quantum grouprelated to Bicrossproduct quantum groupsLie0.60section
Quantum grouprelated to Bicrossproduct quantum groupsThey0.60section
Quantum grouprelated to Bicrossproduct quantum groupsMackey0.60section
Quantum grouprelated to Bicrossproduct quantum groupsThe0.60section
Quantum grouprelated to Compact matrix quantum groupsWoronowicz0.60section
Quantum grouprelated to Compact matrix quantum groupsCompact0.60section
Quantum grouprelated to Compact matrix quantum groupsThe0.60section

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