On the structure of the Witt group of braided fusion categories
By Alexei Davydov, D. Nikshych, V. Ostrik. 2011
151 citations recorded by the source corpus.
We analyze the structure of the Witt group $${\mathcal{W}}$$ of braided fusion categories introduced in Davydov et al. (Journal für die reine und angewandte Mathematik (Crelle’s Journal), eprint arXiv: 1009.2117 [math.QA], 2010). We define a “super” version of the categorical Witt group, namely, the group $${s\mathcal{W}}$$ of slightly degenerate braided fusion categories. We prove that $${s\mathcal{W}}$$ 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 $${S : \mathcal{W} \to s\mathcal{W}}$$ is generated by Ising categories and is isomorphic to $${{\mathbb{Z}}/16\mathbb{Z}}$$ . Finally, we give a complete description of étale algebras in tensor products of braided fusion categories.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/7c690eff5e8db6b175354996dbfb907d0319e710
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In Algebra and Number Theory
- Alexei Davydov
- D. Nikshych
- Jürgen Fuchs
- Christoph Schweigert
- Yifan Wang
- Ryan Thorngren
- A. Valentino
- V. Ostrik
In Geometry and Topology
- Alexei Davydov
- Jürgen Fuchs
- Christoph Schweigert
- D. Nikshych
- Ryan Thorngren
- Yifan Wang
- A. Valentino
- Liang Kong
In Statistical and Nonlinear Physics
- Alexei Davydov
- D. Nikshych
- Jürgen Fuchs
- Yifan Wang
- Christoph Schweigert
- Ryan Thorngren
- Peter Schauenburg
Citations in the corpus
- The Picard crossed module of a braided tensor category (2012, background): “Here the tensor product C ⊠Zsym(C) C rev of module categories over a symmetric tensor category Zsym(C) has a natural structure of braided tensor category, see [DNO].”
- Bicategories for Boundary Conditions and for Surface Defects in 3-d TFT (2012, background): “thought of as being secretly Wilson lines inside a defect surface, namely one labeled by the transparent defect TC. Wenext discuss implications tosurface defects separating C fromitself oftheresult of[DNO], reported in Proposition 2.12, that indecomposable C-modules are in bijection to pairs (A1,A2)”
- Gapped boundary phases of topological insulators via weak coupling (2016, unknown): “[75].”
- Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases (2019, background): “See [13,14,21,30,35,38] for various perspectives on this problem.”