Quantum Groups

Name: Quantum Groups
Price: 70.42 USD
Availability: InStock
ISBN: 9780387943701

ISBN-10: 0387943706

ISBN-13: 9780387943701

Edition: 1995

Authors: Christian Kassel

List price: $109.99

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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…

Book details

List price: $109.99
Copyright year: 1995
Publisher: Springer New York
Publication date: 11/4/1994
Binding: Hardcover
Pages: 534
Size: 6.10" wide x 9.25" long x 0.47" 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