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Quantum Groups
IRMA Lectures in Mathematics and Theoretical Physics Vol. 12

Quantum Groups

Benjamin Enriquez (IRMA, Strasbourg, France)

ISBN print 978-3-03719-047-0, ISBN online 978-3-03719-547-5
DOI 10.4171/047
June 2008, 140 pages, softcover, 17.0 x 24.0 cm.
38.00 Euro

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 sets 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.

Keywords: Tensor categories, integrable systems, knot invariants

Further Information

Review in Zentralblatt MATH 1138.16001

Review in MR 2435296 (2009f:17001)