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

Kai Wang; Jingcheng Dong; Libin Li

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arXiv · 2609.23559

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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BibTeX RIS

Kai Wang, Jingcheng Dong, Libin Li. 2026-09-20. The Grothendieck Ring of Strictly Weakly Integral Fusion Categories of Rank 6. https://arxiv.org/abs/2609.23559

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