Quantum Groups

Inhaltsverzeichnis

• 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.