Rank-finiteness for modular categories Institutional Repository Document uri icon


  • We prove a rank-finiteness conjecture for modular categories: up to equivalence, there are only finitely many modular categories of any fixed rank. Our technical advance is a generalization of the Cauchy theorem in group theory to the context of spherical fusion categories. For a modular category $mathcal{C}$ with $N=ord(T)$, the order of the modular $T$-matrix, the Cauchy theorem says that the set of primes dividing the global quantum dimension $D^2$ in the Dedekind domain $mathbb{Z}[e^{frac{2pi i}{N}}]$ is identical to that of $N$.

author list (cited authors)

  • Bruillard, P., Ng, S., Rowell, E. C., & Wang, Z.

citation count

  • 0

complete list of authors

  • Bruillard, Paul||Ng, Siu-Hung||Rowell, Eric C||Wang, Zhenghan

Book Title

  • arXiv

publication date

  • October 2013