The Witt group of non-degenerate braided fusion categories

By Alexei Davydov, Michael Mueger, D. Nikshych, V. Ostrik. 2010

357 citations recorded by the source corpus.

Abstract 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.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5e6257b33b90b9031c6af8d140084b874acf3705

How researchers see this paper

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In Geometry and Topology

1. Alexei Davydov
2. Yifan Wang
3. Ryan Thorngren

In Mathematical Physics

1. Alexei Davydov
2. Yifan Wang
3. Ryan Thorngren

In Statistical and Nonlinear Physics

1. Alexei Davydov
2. Yifan Wang
3. Ryan Thorngren

Citations in the corpus

• 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.”
• Tensor categories (2023, background): “…an incompressible braided finite tensor category C there should be no non-trivial separable commutative algebras A in C with C ( I, A ) = k ( complete anisotropy of C , see [Davydov et al (2013 Completely anisotropic braided finite tensor categories are either non-degenerate or slightly-degenerate.”