On the classification of certain fusion categories

D. Jordan, E. Larson

Research output: Contribution to journalArticlepeer-review

Abstract

We advance the classification of fusion categories in two directions. Firstly, we completely classify integral fusion categories - and consequently, semi-simple Hopf algebras - of dimension pq, where p and q are distinct primes. This case is especially interesting because it is the simplest class of dimensions where not all integral fusion categories are group- theoretical. Secondly, we classify a certain family of Z/3Z-graded fusion categories, which are generalizations of the Z/2Z-graded Tambara-Yamagami categories. Our proofs are based on the recently developed theory of extensions of fusion categories.
Original languageEnglish
Pages (from-to)481-499
Number of pages19
JournalJournal of Noncommutative Geometry
Volume3
Issue number3
DOIs
Publication statusPublished - 2009

Keywords

  • Fusion categories
  • Tambara–Yamagami categories
  • finite dimensional Hopf algebras

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