Tambara-Yamagami Categories over the Reals: The Non-Split Case
Quantum Algebra
2024-06-21 v3 Category Theory
Abstract
Tambara and Yamagami investigated a simple set of fusion rules with only one non-invertible object, and proved under which circumstances those rules could be given a coherent associator. 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 objects are either real, complex, or quaternionic. In this context, we prove a similar categorification result to the one of Tambara and Yamagami.
Keywords
Cite
@article{arxiv.2303.17843,
title = {Tambara-Yamagami Categories over the Reals: The Non-Split Case},
author = {Julia Plavnik and Sean Sanford and Dalton Sconce},
journal= {arXiv preprint arXiv:2303.17843},
year = {2024}
}
Comments
44 pages; Corrected Theorem 7.1, added Example 7.5