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arXiv · 1109.5558

On the structure of the Witt group of braided fusion categories

Alexei Davydov·Dmitri Nikshych·Victor Ostrik
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Abstract

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.

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Alexei Davydov, Dmitri Nikshych, Victor Ostrik. 2011-09-26. On the structure of the Witt group of braided fusion categories. https://arxiv.org/abs/1109.5558

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