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.
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.
