On the structure of the Witt group of braided fusion categories

Details On the structure of the Witt group of braided fusion categories On the structure of the Witt group of braided fusion categories

2011-09-26

arxiv.org/abs/1109.5558v1

Mathematics

Quantum Algebra

27 pages

Scientific paper

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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