Quantum Groups

Christian Kassel

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English

Springer-Verlag New York Inc.
08 October 2012

Algebraic topology; Condensed matter physics (liquid state & solid state physics); Quantum physics (quantum mechanics & quantum field theory); Materials science

Series: Graduate Texts in Mathematics

Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups attached to SL2 as well as the basic concepts of the theory of Hopf algebras. Coverage also focuses on Hopf algebras that produce solutions of the Yang-Baxter equation and provides an account of Drinfeld's elegant treatment of the monodromy of the Knizhnik-Zamolodchikov equations.

By: Christian Kassel
Imprint: Springer-Verlag New York Inc.
Country of Publication: United States
Edition: Softcover reprint of the original 1st ed. 1995
Volume: 155
Dimensions: Height: 235mm, Width: 155mm, Spine: 28mm
Weight: 836g
ISBN: 9781461269007
ISBN 10: 1461269008
Series: Graduate Texts in Mathematics
Pages: 534
Publication Date: 08 October 2012
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Content.- One Quantum SL(2).- I Preliminaries.- II Tensor Products.- III The Language of Hopf Algebras.- IV The Quantum Plane and Its Symmetries.- V The Lie Algebra of SL(2).- VI The Quantum Enveloping Algebra of sl(2).- VII A Hopf Algebra Structure on Uq(sl(2)).- Two Universal R-Matrices.- VIII The Yang-Baxter Equation and (Co)Braided Bialgebras.- IX Drinfeld’s Quantum Double.- Three Low-Dimensional Topology and Tensor Categories.- X Knots, Links, Tangles, and Braids.- XI Tensor Categories.- XII The Tangle Category.- XIII Braidings.- XIV Duality in Tensor Categories.- XV Quasi-Bialgebras.- Four Quantum Groups and Monodromy.- XVI Generalities on Quantum Enveloping Algebras.- XVII Drinfeld and Jimbo’s Quantum Enveloping Algebras.- XVIII Cohomology and Rigidity Theorems.- XIX Monodromy of the Knizhnik-Zamolodchikov Equations.- XX Postlude A Universal Knot Invariant.- References.

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Quantum Groups

Christian Kassel

$183.95 $147.13

Paperback

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