Quantum Groups

AvChristian Kassel

Häftad, Engelska, 2012

Del 155 i serien Graduate Texts in Mathematics

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Beskrivning

Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups attached to SL2 as well as the basic concepts of the theory of Hopf algebras. Coverage also focuses on Hopf algebras that produce solutions of the Yang-Baxter equation and provides an account of Drinfeld's elegant treatment of the monodromy of the Knizhnik-Zamolodchikov equations.

Produktinformation

Utgivningsdatum:2012-10-08
Mått:155 x 235 x 30 mm
Vikt:826 g
Format:Häftad
Språk:Engelska
Serie:Graduate Texts in Mathematics
Antal sidor:534
Förlag:Springer-Verlag New York Inc.
ISBN:9781461269007

Utforska kategorier

Topologi inom Naturvetenskap och teknik
Materietillstånd inom Naturvetenskap och teknik
Kvantfysik inom Naturvetenskap och teknik

Innehållsförteckning

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.