Computations in Symmetric Fusion Categories in Characteristic
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Author(s)
Ostrik, Victor
Etingof, Pavel I
Venkatesh, Siddharth Narayan
Date Issued
May 2016
Journal
International Mathematics Research Notices
Publisher
Oxford University Press (OUP)
Citation
Etingof, Pavel et al. “Computations in Symmetric Fusion Categories in Characteristicp.” International Mathematics Research Notices 2017, 2 (May 2016): 468–489 © 2016 The Authors
Version
Original manuscript
Abstract
We study properties of symmetric fusion categories in characteristic p. In particular, we introduce the notion of a super Frobenius-Perron dimension of an object X of such a category and derive an explicit formula for the Verlinde fiber functor F(X) of X (defined by the 2nd author) in terms of the usual and super Frobenius-Perron dimensions of X. We also compute the decomposition of symmetric powers of objects of the Verlinde category, generalizing a classical formula of Cayley and Sylvester for invariants of binary forms. Finally, we show that the Verlinde fiber functor is unique and classify braided fusion categories of rank 2 and triangular semisimple Hopf algebras in any characteristic.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1093/IMRN/RNW024
