A finiteness property for braided fusion categories

Details A finiteness property for braided fusion categories A finiteness property for braided fusion categories

2009-03-24

arxiv.org/abs/0903.4157v4

Algebr. and Represent. Theor. 14 (2011), no. 5, 837-855

Mathematics

Quantum Algebra

21 pages; v3: proof of Theorem 4.2 clarified, Section 5 revised and strengthened; v4: minor revisions

Scientific paper

We introduce a finiteness property for braided fusion categories, describe a conjecture that would characterize categories possessing this, and verify the conjecture in a number of important cases. In particular we say a category has F if the associated braid group representations factor over a finite group, and suggest that categories of integral Frobenius-Perron dimension are precisely those with property F.

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