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arXiv · 2602.07946

Reflection Theory of Nichols Algebras over Coquasi-Hopf Algebras with Bijective Antipode

Bowen Li·Gongxiang Liu
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Abstract

We investigate the reflection theory of Nichols algebras over arbitrary coquasi-Hopf algebras with bijective antipode, generalizing previous results restricted to the pointed cosemisimple setting [47]. By establishing a braided monoidal equivalence between categories of rational Yetter-Drinfeld modules via a dual pair, we demonstrate that a tuple of finite-dimensional irreducible Yetter-Drinfeld modules admitting all reflections gives rise to a semi-Cartan graph. As an application, we consider an explicit example of a rank three Nichols algebra from [41]. We show that it yields a standard Cartan graph and prove that it is, in fact, an affine Nichols algebra.

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BibTeXRIS

Bowen Li, Gongxiang Liu. 2026-02-08. Reflection Theory of Nichols Algebras over Coquasi-Hopf Algebras with Bijective Antipode. https://arxiv.org/abs/2602.07946

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