# Quantum Groups

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*Benjamin Enriquez*

A publication of the European Mathematical Society

The volume starts with a lecture course by P. Etingof on
tensor categories (notes by D. Calaque). This course is an
introduction to tensor categories, leading to topics of recent
research such as realizability of fusion rings, Ocneanu rigidity,
module categories, weak Hopf algebras, Morita theory for tensor
categories, lifting theory, categorical dimensions,
Frobenius–Perron dimensions, and the classification of tensor
categories.

The remainder of the book consists of three detailed expositions on
associators and the Vassiliev invariants of knots, classical and quantum
integrable systems and elliptic algebras, and the groups of algebra
automorphisms of quantum groups. The preface puts the results presented in
perspective.

Directed at research mathematicians and theoretical physicists as well as
graduate students, the volume gives an overview of the ongoing research in the
domain of quantum groups, an important subject of current mathematical physics.

A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in mathematicial physics.