Classification of fusion categories of dimension pq
| dc.creator | Etingof, Pavel | |
| dc.creator | Gelaki, Shlomo | |
| dc.creator | Ostrik, Viktor | |
| dc.date | 2003-04-15 | |
| dc.date | 2003-05-30 | |
| dc.date.accessioned | 2026-07-07T04:56:53Z | |
| dc.date.available | 2026-07-07T04:56:53Z | |
| dc.description | In this paper we provide a complete classification of fusion categories of Frobenius-Perron (FP) dimension pq, where p<q are distinct primes, thus giving a categorical generalization of math.QA/9801129. As a corollary we also obtain the classification of semisimple quasi-Hopf algebras of dimension pq. A concise formulation of our main result is: Let C be a fusion category over the complex numbers of FP dimension pq. Then either p=2 and C is a Tambara-Yamagami category of dimension 2q, or C is group-theoretical in the sense of math.QA/0203060 (which easily yields the full classification). As a by-product, we obtain the classification of finite dimensional semisimple quasi-Hopf (in particular, Hopf) algebras whose irreducible representations have dimensions 1 and n, such that the 1-dimensional representations form a cyclic group of order n. All such quasi-Hopf algebras turn out to be group-theoretical. We also classify fusion categories whose invertible objects form a cyclic group of order n>1 and which have only one non-invertible object of dimension n. | |
| dc.description | 12 pages, latex; Corollary 7.4 was added | |
| dc.identifier | https://arxiv.org/abs/math/0304194 | |
| dc.identifier | http://arxiv.org/abs/math/0304194 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67082 | |
| dc.subject | Quantum Algebra | |
| dc.title | Classification of fusion categories of dimension pq | |
| dc.type | text |