秩为6的严格弱整融合范畴的Grothendieck环
The Grothendieck Ring of Strictly Weakly Integral Fusion Categories of Rank 6
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中文总结 AI 辅助
本文对秩6严格弱整融合范畴的Grothendieck环进行了完整分类，得到12个候选环，其中8个可实现，4个被排除，并完成了秩至多6的分类。
中文摘要 AI 辅助
本文研究了秩为6的严格弱整融合范畴，并给出了其Grothendieck环的完整分类。我们得到了十二个候选Grothendieck环。其中八个可由融合范畴实现，而其余四个被范畴化的必要障碍所排除。结合已有结果，这完成了秩至多6的严格弱整融合范畴的Grothendieck环的分类。
英文摘要
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.
发表机构
- College of Mathematical Science, Yangzhou University（扬州大学数学科学学院）
- College of Mathematics and Statistics, Nanjing University of Information Science and Technology（南京信息工程大学数学与统计学院）
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