Quantum Groups / Edition 1

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More About This Textbook

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.

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Product Details

  • ISBN-13: 9780387943701
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 11/4/1994
  • Series: Graduate Texts in Mathematics Series , #155
  • Edition description: 1995
  • Edition number: 1
  • Pages: 564
  • Product dimensions: 1.25 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Preface
Pt. 1 Quantum SL(2) 1
I Preliminaries 3
II Tensor Products 23
III The Language of Hopf Algebras 39
IV The Quantum Plane and Its Symmetries 72
V The Lie Algebra of SL(2) 93
VI The Quantum Enveloping Algebra of sl(2) 121
VII A Hopf Algebra Structure on U[subscript q](sl(2)) 140
Pt. 2 Universal R-Matrices 165
VIII The Yang-Baxter Equation and (Co)Braided Bialgebras 167
IX Drinfeld's Quantum Double 199
Pt. 3 Low-Dimensional Topology and Tensor Categories 239
X Knots, Links, Tangles, and Braids 241
XI Tensor Categories 275
XII The Tangle Category 294
XIII Braidings 314
XIV Duality in Tensor Categories 339
XV Quasi-Bialgebras 368
Pt. 4 Quantum Groups and Monodromy 383
XVI Generalities on Quantum Enveloping Algebras 385
XVII Drinfeld and Jimbo's Quantum Enveloping Algebras 403
XVIII Cohomology and Rigidity Theorems 420
XIX Monodromy of the Knizhnik-Zamolodchikov Equations 449
XX Postlude. A Universal Knot Invariant 484
References 506
Index 523
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