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 pq2, 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.
Cite this article
David Jordan, Eric Larson, On the classification of certain fusion categories. J. Noncommut. Geom. 3 (2009), no. 3, pp. 481–499DOI 10.4171/JNCG/44