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PreprintCC BY 4.0arXiv

The Grothendieck Ring of Strictly Weakly Integral Fusion Categories of Rank 6

  • Kai Wang
  • Jingcheng Dong
  • Libin Li
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Abstract

In this paper, we study strictly weakly integral fusion categories of rank 6 and give a complete classification of their Grothendieck rings. We obtain twelve candidate Grothendieck rings. Eight of them can be realized by fusion categories, while the remaining four are ruled out by necessary obstructions to categorification. Together with previously known results, this completes the classification of Grothendieck rings of strictly weakly integral fusion categories of rank at most 6.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026grothendieck,
  title = {{The Grothendieck Ring of Strictly Weakly Integral Fusion Categories of Rank 6}},
  author = {Kai Wang and Jingcheng Dong and Libin Li},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23559},
  eprint = {2609.23559},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23559},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Grothendieck Ring of Strictly Weakly Integral Fusion Categories of Rank 6
AU  - Kai Wang
AU  - Jingcheng Dong
AU  - Libin Li
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23559
UR  - https://arxiv.org/abs/2609.23559
AB  - In this paper, we study strictly weakly integral fusion categories of rank 6 and give a complete classification of their Grothendieck rings. We obtain twelve candidate Grothendieck rings. Eight of them can be realized by fusion categories, while the remaining four are ruled out by necessary obstructions to categorification. Together with previously known results, this completes the classification of Grothendieck rings of strictly weakly integral fusion categories of rank at most 6.
ER  -