Lectures on tensor categories

Damien Calaque (1) , Pavel Etingof

1 IRMA - Institut de Recherche Mathématique Avancée

We give a review of some recent developments in the theory of tensor categories. The topics include realizability of fusion rings, Ocneanu rigidity, module categories, weak Hopf algebras, Morita theory for tensor categories, lifting theory, categorical dimensions, Frobenius- Perron dimensions, classification of tensor categories.

Domaines: Algèbres quantiques [math.QA]

Damien Calaque, Pavel Etingof. Lectures on tensor categories. Benjamin Enriquez. Quantum Groups, EMS Publishing House, pp.1-38, 2008, IRMA Lectures in Mathematics and Theoretical Physics Vol. 12, 978-3-03719-547-5. ⟨10.4171/047-1/1⟩. ⟨hal-00111684⟩