On Vafa's theorem for tensor categories
| dc.creator | Etingof, Pavel | |
| dc.date | 2002-07-01 | |
| dc.date.accessioned | 2026-07-07T04:49:28Z | |
| dc.date.available | 2026-07-07T04:49:28Z | |
| dc.description | In this note we prove two main results. 1. In a rigid braided finite tensor category over C (not necessarily semisimple), some power of the Casimir element and some even power of the braiding is unipotent. 2. In a (semisimple) modular category, the twists are roots of unity dividing the algebraic integer D^{5/2}, where D is the global dimension of the category (the sum of squares of dimensions of simple objects). Both results generalize Vafa's theorem, saying that in a modular category twists are roots of unity, and square of the braiding has finite order. We also discuss the notion of the quasi-exponent of a finite rigid tensor category, which is motivated by results 1 and 2 and the paper math/0109196 of S.Gelaki and the author. | |
| dc.description | 6 pages, latex | |
| dc.identifier | https://arxiv.org/abs/math/0207007 | |
| dc.identifier | http://arxiv.org/abs/math/0207007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64435 | |
| dc.subject | Quantum Algebra | |
| dc.title | On Vafa's theorem for tensor categories | |
| dc.type | text |