The Witt group of non-degenerate braided fusion categories
Alexei Davydov, Michael Mueger, Dmitri Nikshych, Victor Ostrik
TL;DR
This paper characterizes Drinfeld centers of fusion categories as non-degenerate braided fusion categories with Lagrangian algebras and explores their structure through a Witt group analogy.
Contribution
It provides a new characterization of Drinfeld centers and introduces a Witt group-like structure for non-degenerate braided fusion categories.
Findings
Drinfeld centers characterized by Lagrangian algebras
The quotient monoid exhibits properties similar to the classical Witt group
Establishment of a Witt group framework for braided fusion categories
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.
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