Quantum Groups: v. 155 (Graduate Texts in Mathematics) - Hardcover

Kassel, Christian

Hardcover

ISBN 10: 3540943706 ISBN 13: 9783540943709

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1994

Synopsis

This introduction to the theory of quantum groups emphasizes the connection to knot theory and Drinfeld's recent fundamental contributions. The first part focuses on the basic concepts of the theory of Hopf algebras. Part 2 examines Hopf algebras that produce solutions to the Yang-Baxter equation, and Drinfeld's quantum double construction. Isotopy invariants of knots and links in the three-dimensional Euclidean space are then constructed, using the language of tensor categories. The text concludes with an account of Drinfeld's treatment of the monodromy of the Knizhnik-Zamolodchikov Equations, culminating in the construction of Kontsevich's universal knot invariant.

About this title

From the Back Cover:

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 SL(subscript 2) 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.

About this edition

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1994
• ISBN 10: 3540943706
• ISBN 13: 9783540943709
• Binding: Hardcover
• Number of pages: 543