The Witt group of non-degenerate braided fusion categories

We give a characterization of Drinfeld centers of fusion categories as non-degenerate braided fusion categories containing a Lagrangian algebra. Further we study the quotient of the monoid of non-degenerate braided fusion categories modulo the submonoid of the Drinfeld centers and show that its form...

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Bibliographic Details
Published in:Journal für die reine und angewandte Mathematik 2013-04, Vol.2013 (677), p.135-177
Main Authors: Davydov, Alexei, Müger, Michael, Nikshych, Dmitri, Ostrik, Victor
Format: Article
Language:English
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Summary:We give a characterization of Drinfeld centers of fusion categories as non-degenerate braided fusion categories containing a Lagrangian algebra. Further we study the quotient of the monoid of non-degenerate braided fusion categories modulo the submonoid of the Drinfeld centers and show that its formal properties are similar to those of the classical Witt group.
ISSN:0075-4102
1435-5345
DOI:10.1515/crelle.2012.014