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arXiv · 2611.08900

Reflections of Nichols algebras in braided monoidal categories

Bowen Li
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Abstract

Let $\C$ be an essentially small abelian rigid braided monoidal category. We prove a reflection theorem for Nichols algebras in $\Ind(\C)$ and show that tuples admitting all reflections define connected semi-Cartan graphs. As applications, we prove that a finite Nichols algebra has a generating object of length at most one in $PSU(2)_k$ for odd $k\ge3$, in $SU(2)_{4m}$ for $m\ge1$, and in the representation categories of the Virasoro minimal models $\mathcal M(2,p)$ for odd $p\ge5$. In all three families, we prove that every finite pre-Nichols algebra is a Nichols algebra.

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Bowen Li. 2026-11-06. Reflections of Nichols algebras in braided monoidal categories. https://arxiv.org/abs/2611.08900

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