English

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