Work

Tambara–Yamagami categories over the reals: The nonsplit case

Year: 2025

Type: article

Abstract: Tambara and Yamagami investigated a simple set of fusion rules with only one noninvertible object, and proved under which circumstances those rules could be given a coherent associator. They also classified all of the resulting fusion categories up to monoidal equivalence. We consider a generalization of such fusion rules to the setting where simple objects are no longer required to be split simple. Over the real numbers, this means that simple objects are either real, complex, or quaternionic. In this context, we prove a similar categorification result to the one of Tambara and Yamagami.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70355

Authors: Julia Plavnik, Sean Sanford, Dalton Sconce

Institutions: Vrije Universiteit Brussel, Indiana University Bloomington, Indiana University, University of Edinburgh

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, Simons Foundation

Awards: CAREER: Cohomology, classification, and constructions of tensor categories, REU Site: Research Experiences for Undergraduates in Mathematics at Indiana University, Quantum Symmetries: tensor categories, braids, and Hopf algebras, Programs on Critical Problems in Physics, Astrophysics and Biophysics at the Aspen Center for Physics, G986786885