Lectures on tensor categories

Abstract

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.

30 pages, latex

Cited by in corpus (15)

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• TFT construction of RCFT correlators III: Simple currents
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• Tensor C*-categories arising as bimodule categories of II_1 factors
• Drinfeld associators, braid groups and explicit solutions of the Kashiwara-Vergne equations
• A Monoidal Category for Perturbed Defects in Conformal Field Theory
• The quasi-Hopf analogue of $u_q(s{l}_2)$
• From Projective Representations to Quasi-Quantum Groups
• Quasi-Frobenius-Lusztig kernels for simple Lie algebras
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• On second cohomology of duals of compact groups
• Graded medial $n$-ary algebras and polyadic tensor categories
• Yetter-Drinfel'd algebras and coideals of Weak Hopf $C^{\ast }$-Algebras