**Contemporary Mathematics**

Volume: 294;
2002;
266 pp;
Softcover

MSC: Primary 16; 17; 20; 81; 46; 82; 18;

Print ISBN: 978-0-8218-2655-3

Product Code: CONM/294

List Price: $84.00

AMS Member Price: $67.20

MAA Member Price: $75.60

**Electronic ISBN: 978-0-8218-7884-2
Product Code: CONM/294.E**

List Price: $84.00

AMS Member Price: $67.20

MAA Member Price: $75.60

# Quantum Symmetries in Theoretical Physics and Mathematics

Share this page *Edited by *
*Robert Coquereaux; Ariel García; Roberto Trinchero*

This volume presents articles from several lectures presented at the school on
“Quantum Symmetries in Theoretical Physics and Mathematics” held in
Bariloche, Argentina. The various lecturers provided significantly different
points of view on several aspects of Hopf algebras, quantum group theory, and
noncommutative differential geometry, ranging from analysis, geometry, and
algebra to physical models, especially in connection with integrable systems
and conformal field theories.

Primary topics discussed in the text include subgroups of quantum
\(SU(N)\), quantum ADE classifications and generalized Coxeter systems,
modular invariance, defects and boundaries in conformal field theory, finite
dimensional Hopf algebras, Lie bialgebras and Belavin-Drinfeld triples, real
forms of quantum spaces, perturbative and non-perturbative Yang-Baxter
operators, braided subfactors in operator algebras and conformal field theory,
and generalized (\(d^N\)) cohomologies.

#### Readership

Graduate students, research mathematicians, and physicists interested in Hopf algebras, quantum groups, Von Neumann algebras, subfactors and noncommutative differential geometry or on the connections between the previous concepts and conformal field theories or integrable systems.

# Table of Contents

## Quantum Symmetries in Theoretical Physics and Mathematics

- Contents vii8 free
- Foreword ix10 free
- List of participants xii13 free
- Symétries quantiques en physique théorique et en mathématiques xxi22 free
- Quantum symmetries in theoretical physics and mathematics xxv26 free
- About finite dimensional Hopf algebras 128 free
- Lectures on differentials, generalized differentials and on some examples related to theoretical physics 5986
- Modular invariants from subfactors 95122
- The classification of subgroups of quantum SU (N) 133160
- Uses of quantum spaces 161188
- CFT, BCFT, ADE and all that 233260