PreprintCC BY 4.0arXiv
Grothendieck rings of near-Tambara--Yamagami fusion categories
Abstract
We determine the Grothendieck rings of fusion categories over 𝒞 containing a nonpointed Tambara--Yamagami fusion subcategory and exactly one further simple object. The subcategory necessarily has rank five, its invertible objects form the Klein four-group, and the coefficient κ of the additional simple object in its tensor square belongs to {0,2,7}. Each of these three based rings is categorifiable. For κ=0, every category belongs, up to tensor equivalence, to the rank-one odd-component extension list of Choi--Lu--Sun. For κ=2 we construct an explicit unitary group-theoretical realization, and for κ=7 a realization is Rep(PSU(3,2)).
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BibTeX
@misc{dong2026grothendieck,
title = {{Grothendieck rings of near-Tambara--Yamagami fusion categories}},
author = {Jingcheng Dong and Sébastien Palcoux and Kai Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35574},
eprint = {2610.35574},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35574},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Grothendieck rings of near-Tambara--Yamagami fusion categories
AU - Jingcheng Dong
AU - Sébastien Palcoux
AU - Kai Wang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35574
UR - https://arxiv.org/abs/2610.35574
AB - We determine the Grothendieck rings of fusion categories over 𝒞 containing a nonpointed Tambara--Yamagami fusion subcategory and exactly one further simple object. The subcategory necessarily has rank five, its invertible objects form the Klein four-group, and the coefficient κ of the additional simple object in its tensor square belongs to {0,2,7}. Each of these three based rings is categorifiable. For κ=0, every category belongs, up to tensor equivalence, to the rank-one odd-component extension list of Choi--Lu--Sun. For κ=2 we construct an explicit unitary group-theoretical realization, and for κ=7 a realization is Rep(PSU(3,2)).
ER -