Overview

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.

Full Product Details

Author:   Christian Kassel
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1995 ed.
Volume:   155
Dimensions:   Width: 15.50cm , Height: 3.00cm , Length: 23.50cm
Weight:   2.090kg
ISBN:  

9780387943701

ISBN 10:   0387943706
Pages:   534
Publication Date:   04 November 1994
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

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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