Quantum groups : proceedings of the 8th International Workshop on Mathematical Physics, held at the Arnold Sommerfeld Institute, Clausthal, FRG, on 19-26 July 1989 / H.-D. Doebner, J.-D. Henning (eds.).

By: (8th : International Workshop on Mathematical Physics (8th : 1989 : Arnold Sommerfeld Institute)
Contributor(s): Doebner, H. D. (Heinz Dietrich), 1931- | Henning, Jörg
Material type: TextTextSeries: Lecture notes in physics: 370.Publisher: Berlin ; New York : Springer-Verlag, ©1990Description: 1 online resource (x, 434 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783540466475; 3540466479Subject(s): Quantum groups -- Congresses | Yang-Baxter equation -- Congresses | Quantum field theory -- Congresses | Mathematical physics -- Congresses | Mathematical physics | Quantum field theory | Quantum groups | Yang-Baxter equation | Kwantumgroepen | Quantengruppe | Kongress | Gruppe Mathematik | Quantentheorie | QuantenmechanikGenre/Form: Electronic books. | Conference papers and proceedings. Additional physical formats: Print version:: Quantum groups.DDC classification: 530.1/43 LOC classification: QC20.7.G76 | I59 1989Other classification: 33.06 Online resources: Click here to access online
Contents:
To quantum groups -- Mathematical guide to quantum groups -- A q-boson realization of the quantum group SU q (2) and the theory of q-tensor operators -- Polynomial basis for SU(2)q and Clebsch-Gordan coefficients -- U q (sl(2)) Invariant operators and reduced polynomial identities -- Classification and characters of Uq(sl(3, C))representations -- Extremal projectors for quantized kac-moody superalgebras and some of their applications -- Yang-Baxter algebras, integrable theories and Betre Ansatz -- Yang-Baxter algebra -- Bethe Ansatz -- conformal quantum field theories -- quantum groups -- Classical Yang-Baxter equations and quantum integrable systems (Gaudin models) -- Quantum groups as symmetries of chiral conformal algebras -- Comments on rational conformal field theory, quantum groups and tower of algebras -- Chern-Simons field theory and quantum groups -- Quantum symmetry associated with braid group statistics -- Sum rules for spins in (2 + 1)-dimensional quantum field theory -- Anomalies from the phenomenological and geometrical points of view -- KMS states, cyclic cohomology and supersymmetry -- Gauge theories based on a non-commutative geometry -- Algebras symmetries spaces.
Action note: digitized 2010 committed to preserveSummary: A thorough analysis of exactly soluble models in nonlinear classical systems and in quantum systems as well as recent studies in conformal quantum field theory have revealed the structure of quantum groups to be an interesting and rich framework for mathematical and physical problems. In this book, for the first time, authors from different schools review in an intelligible way the various competing approaches: inverse scattering methods, 2-dimensional statistical models, Yang-Baxter algebras, the Bethe ansatz, conformal quantum field theory, representations, braid group statistics, noncommutative geometry, and harmonic analysis.
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A thorough analysis of exactly soluble models in nonlinear classical systems and in quantum systems as well as recent studies in conformal quantum field theory have revealed the structure of quantum groups to be an interesting and rich framework for mathematical and physical problems. In this book, for the first time, authors from different schools review in an intelligible way the various competing approaches: inverse scattering methods, 2-dimensional statistical models, Yang-Baxter algebras, the Bethe ansatz, conformal quantum field theory, representations, braid group statistics, noncommutative geometry, and harmonic analysis.

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To quantum groups -- Mathematical guide to quantum groups -- A q-boson realization of the quantum group SU q (2) and the theory of q-tensor operators -- Polynomial basis for SU(2)q and Clebsch-Gordan coefficients -- U q (sl(2)) Invariant operators and reduced polynomial identities -- Classification and characters of Uq(sl(3, C))representations -- Extremal projectors for quantized kac-moody superalgebras and some of their applications -- Yang-Baxter algebras, integrable theories and Betre Ansatz -- Yang-Baxter algebra -- Bethe Ansatz -- conformal quantum field theories -- quantum groups -- Classical Yang-Baxter equations and quantum integrable systems (Gaudin models) -- Quantum groups as symmetries of chiral conformal algebras -- Comments on rational conformal field theory, quantum groups and tower of algebras -- Chern-Simons field theory and quantum groups -- Quantum symmetry associated with braid group statistics -- Sum rules for spins in (2 + 1)-dimensional quantum field theory -- Anomalies from the phenomenological and geometrical points of view -- KMS states, cyclic cohomology and supersymmetry -- Gauge theories based on a non-commutative geometry -- Algebras symmetries spaces.

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