Keyword

quantum groups

Description: Quantum groups are algebraic structures that generalize groups and Lie algebras, used in mathematical physics, representation theory, and integrable systems.

Primary topic: Algebraic structures and combinatorial models (51%)

Wikidata ID: wiki/Q2122223

OpenAlex ID: keywords/quantum-groups

Quantum Groups

1994 · Christian Kassel · 4,191

Aq-difference analogue of U(g) and the Yang-Baxter equation

1985 · Michio Jimbo · Letters in Mathematical Physics · 2,599

Hopf Algebras and Their Actions on Rings

1993 · Susan Montgomery · Regional conference series in mathematics · 2,357

Gravitation, an introduction to current research

1963 · G.L. Sewell · Journal of the Franklin Institute · 1,942

Foundations of Quantum Group Theory

1995 · Shahn Majid · Cambridge University Press eBooks · 1,941

A guide to quantum groups

1994 · Vyjayanthi Chari, Andrew Pressley · CERN Document Server (European Organization for Nuclear Research) · 1,784

Introduction to Quantum Groups

2010 · George Lusztig · Birkhäuser Boston eBooks · 1,604

On q-analogues of the quantum harmonic oscillator and the quantum group SU(2) q

1989 · A J Macfarlane · Journal of Physics A Mathematical and General · 1,560

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Invariants of 3-manifolds via link polynomials and quantum groups

1991 · N. Reshetikhin, V. G. Turaev · Inventiones mathematicae · 1,492

Representations of Algebraic Groups

2007 · Jens Jantzen · Mathematical surveys and monographs · 1,483

A q-analogue of U(g[(N+1)), Hecke algebra, and the Yang-Baxter equation

1986 · Michio Jimbo · Letters in Mathematical Physics · 1,436

Quantum Groups and Their Representations

1997 · Anatoli Klimyk, Konrad Schmüdgen · Springer eBooks · 1,170

State sum invariants of 3-manifolds and quantum 6j-symbols

1992 · V.G. Turaev, O.Y. Viro · Topology · 1,144

Quantization of Lie Groups and Lie Algebras

1988 · L.D. Faddeev, N.Yu. Reshetikhin, et al. · Elsevier eBooks · 1,138

Quantum Groups

1995 · Christian Kassel · Graduate texts in mathematics · 1,129

On crystal bases of the Q-analogue of universal enveloping algebras

1991 · M. Kashiwara · Duke Mathematical Journal · 1,123

An Introduction to Noncommutative Noetherian Rings

2004 · K. R. Goodearl, R. B. Warfield, Jr · Cambridge University Press eBooks · 1,121

Canonical Bases Arising from Quantized Enveloping Algebras

1990 · G. Lusztig · Journal of the American Mathematical Society · 1,068

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Differential calculus on compact matrix pseudogroups (quantum groups)

1989 · S. L. Woronowicz · Communications in Mathematical Physics · 1,059

Ribbon graphs and their invaraints derived from quantum groups

1990 · N. Y. Reshetikhin, V. G. Turaev · Communications in Mathematical Physics · 1,010

Koszul Duality Patterns in Representation Theory

1996 · Alexander Beilinson, Victor Ginzburg, et al. · Journal of the American Mathematical Society · 919

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Yang-Baxter equation and representation theory: I

1981 · P. P. Kulish, N. Yu. Reshetikhin, et al. · Letters in Mathematical Physics · 885

Hopf Algebras and the Quantum Yang-baxter Equation

1990 · V. G. DRINFEL'D · Advanced series in mathematical physics · 861

Common structures between finite systems and conformal field theories through quantum groups

1990 · V. Pasquier, H. Saleur · Nuclear Physics B · 848

Quantum Invariants of Knots and 3-Manifolds

2010 · Vladimir G. Turaev · De Gruyter eBooks · 841

Works count: 14,600

Citation count: 196,200