Quantum Groups

Content. - One Quantum SL(2). - I Preliminaries. - II Tensor Products. - III The Language of Hopf Algebras. - IV The Quantum Plane and Its Symmetries. - V The Lie Algebra of SL(2). - VI The Quantum Enveloping Algebra of sl(2). - VII A Hopf Algebra Structure on Uq(sl(2)). - Two Universal R-Matrices. - VIII The Yang-Baxter Equation and (Co)Braided Bialgebras. - IX Drinfeld's Quantum Double. - Three Low-Dimensional Topology and Tensor Categories. - X Knots Links Tangles and Braids. - XI Tensor Categories. - XII The Tangle Category. - XIII Braidings. - XIV Duality in Tensor Categories. - XV Quasi-Bialgebras. - Four Quantum Groups and Monodromy. - XVI Generalities on Quantum Enveloping Algebras. - XVII Drinfeld and Jimbo's Quantum Enveloping Algebras. - XVIII Cohomology and Rigidity Theorems. - XIX Monodromy of the Knizhnik-Zamolodchikov Equations. - XX Postlude A Universal Knot Invariant. - References. Language: English