Classification of pivotal tensor categories with fusion rules related to $SO(4)$

Daniel Copeland; Cain Edie-Michell

Classification of pivotal tensor categories with fusion rules related to $SO(4)$

Quantum Algebra 2021-12-23 v1 Category Theory Representation Theory

Authors: Daniel Copeland , Cain Edie-Michell

Abstract

In this paper we classify all semisimple tensor categories with the same fusion rules as $\operatorname{Rep}(SO(4))$ , or one of the associated truncations. We show that such categories are explicitly classified by two non-zero complex numbers. Furthermore we show these tensor categories are always braided, and there exist exactly 8 braidings.

Keywords

pivotal tensor category fusion rules semisimple category braiding rep(so(4)) classification

Cite

@article{arxiv.2112.11633,
  title  = {Classification of pivotal tensor categories with fusion rules related to $SO(4)$},
  author = {Daniel Copeland and Cain Edie-Michell},
  journal= {arXiv preprint arXiv:2112.11633},
  year   = {2021}
}

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14 pages, comments welcome

Classification of pivotal tensor categories with fusion rules related to $SO(4)$

Abstract

Keywords

Cite

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