New York Journal of Mathematics
Volume 22 (2016) 775-800


Paul Bruillard

Rank 4 premodular categories

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Published: August 1, 2016
Keywords: Premodular categories, fusion categories
Subject: 18D10, 16T99

We consider the classification problem for rank 4 premodular categories. We uncover a formula for the 2nd Frobenius-Schur indicator of a premodular category, and complete the classification of rank 4 premodular categories (up to Grothendieck equivalence). In the appendix we show rank finiteness for premodular categories.


PNNL Information Release: PNNL-SA-111549. A portion of this paper was produced at a workshop at the American Institute of Mathematics, whose support and hospitality are gratefully acknowledged. The research described in this paper was, in part, conducted under the Laboratory Directed Research and Development Program at PNNL, a multi-program national laboratory operated by Battelle for the U.S. Department of Energy.

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Pacific Northwest National Lab, 902 Battelle Boulevard, Richland, Washington, U.S.A.