Quantum Groups: With 88 Illustrations
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.
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Review: Quantum GroupsUser Review - jwberryhill - Goodreads
As a student of the subject I found large swaths of this book incomprehensible and/or riddled with errors. This was very frustrating for me as the scope of the book was very compelling, and yet in many crucial places I was unable to parse it. Definitely not recommended for novices. Read full review