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Quantum Groups

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ISBN-10: 0387943706

ISBN-13: 9780387943701

Edition: 1995

Authors: Christian Kassel

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Description:

This book provides an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and on Drinfeld's recent fundamental contributions. The first part presents in detail the quantum groups attached to SL2 as well as the basic concepts of the theory of Hopf algebras. Part Two focuses on Hopf algebras that produce solutions of the Yang-Baxter equation, and on Drinfeld's quantum double construction. In the following part we construct isotopy invariants of knots and links in the three-dimensional Euclidean space, using the language of tensor categories. The last part is an account of Drinfeld's elegant treatment of the monodromy of the Knizhnik-Zamolodchikov equations, culminating in the construction of Kontsevich's universal knot invariant.
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Book details

List price: $99.99
Copyright year: 1995
Publisher: Springer
Publication date: 11/4/1994
Binding: Hardcover
Pages: 534
Size: 6.25" wide x 9.50" long x 1.25" tall
Weight: 2.046
Language: English

Preface
Quantum SL(2)
Preliminaries
Tensor Products
The Language of Hopf Algebras
The Quantum Plane and Its Symmetries
The Lie Algebra of SL(2)
The Quantum Enveloping Algebra of sl(2)
A Hopf Algebra Structure on U[subscript q](sl(2))
Universal R-Matrices
The Yang-Baxter Equation and (Co)Braided Bialgebras
Drinfeld's Quantum Double
Low-Dimensional Topology and Tensor Categories
Knots, Links, Tangles, and Braids
Tensor Categories
The Tangle Category
Braidings
Duality in Tensor Categories
Quasi-Bialgebras
Quantum Groups and Monodromy
Generalities on Quantum Enveloping Algebras
Drinfeld and Jimbo's Quantum Enveloping Algebras
Cohomology and Rigidity Theorems
Monodromy of the Knizhnik-Zamolodchikov Equations
Postlude. A Universal Knot Invariant
References
Index