Computations in Symmetric Fusion Categories in Characteristic
Author(s)
Ostrik, Victor; Etingof, Pavel I; Venkatesh, Siddharth Narayan
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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.
Date issued
2016-05Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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
ISSN
1073-7928
1687-0247