Mathematics – Quantum Algebra
Scientific paper
2005-11-04
Mathematics
Quantum Algebra
22 pages, amslatex
Scientific paper
We describe the exponent of a group-theoretical fusion category $\mathcal C =
\mathcal C(G, \omega, F, \alpha)$ associated to a finite group $G$ in terms of
group cohomology. We show that the exponent of $\C$ divides both $e(\omega)
\exp G$ and $(\exp G)^2$, where $e(\omega)$ is the cohomological order of the
3-cocycle $\omega$. In particular $\exp \C$ divides $(\dim \C)^2$.
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