%0 Journal Article
%T On the structure of the Witt group of braided fusion categories
%A Alexei Davydov
%A Dmitri Nikshych
%A Victor Ostrik
%J Mathematics
%D 2011
%I arXiv
%X We analyze the structure of the Witt group W of braided fusion categories introduced in the previous paper arXiv:1009.2117v2. We define a "super" version of the categorical Witt group, namely, the group sW of slightly degenerate braided fusion categories. We prove that sW is a direct sum of the classical part, an elementary Abelian 2-group, and a free Abelian group. Furthermore, we show that the kernel of the canonical homomorphism S: W --> sW is generated by Ising categories and is isomorphic to Z/16Z. Finally, we give a complete description of etale algebras in tensor products of braided fusion categories.
%U http://arxiv.org/abs/1109.5558v1