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Cours spécialisés - Parutions - 20 (2013)

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Compact quantum groups and Their Representation Categories
Sergey Neshveyev, Lars Tuset
Cours spécialisés 20 (2013), vi+168 pages
Acheter l'ouvrage

Résumé :

Le livre fournit une introduction à la théorie des groupes quantiques compacts, soulignant le rôle du point de vue catégorique dans la construction et l'analyse d'exemples concrets. La théorie générale est développée dans les deux premiers chapitres et est illustrée par une analyse détaillée des groupes quantiques orthogonaux libres et des Drinfeld-Jimbo q-déformations des groupes de Lie semi-simples compacts. Les deux chapitres suivants sont plus spécialisées et se concentrent autour du théorème de Drinfeld-Kohno, présentée du point de vue des algèbres d'opérateurs. Le livre devrait être accessible aux étudiants ayant une connaissance de base des algèbres d'opérateurs et des groupes de Lie semi-simples.

Mots-clefs : groupes quantiques, algèbres d'opérateurs, catégories tensorielles, cohomologie, équations de Knizhnik-Zamolodchikov.

Abstract:
The book provides an introduction to the theory of compact quantum groups, emphasizing the role of the categorical point of view in constructing and analyzing concrete examples. The general theory is developed in the first two chapters and is illustrated with a detailed analysis of free orthogonal quantum groups and the Drinfeld-Jimbo q-deformations of compact semisimple Lie groups. The next two chapters are more specialized and concentrate around the Drinfeld-Kohno theorem, presented from the operator algebraic point of view. The book should be accessible to students with a basic knowledge of operator algebras and semisimple Lie groups.abstract

Keywords: quantum groups, operator algebras, tensor categories, cohomology, Knizhnik-Zamolodchikov equations.

Class. math. : 20G42 (primary), 46L65, 18D10, 17B37.


ISBN : 978-2-85629-777-3
ISSN : 1284-6090
Publié avec le concours de : Fondation Sciences Mathématiques de Paris

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