Reflection Theory of Nichols Algebras over Coquasi-Hopf Algebras with Bijective Antipode
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910042112917504 |
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| author | Li, Bowen Liu, Gongxiang |
| author_facet | Li, Bowen Liu, Gongxiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07946 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reflection Theory of Nichols Algebras over Coquasi-Hopf Algebras with Bijective Antipode Li, Bowen Liu, Gongxiang Quantum Algebra Representation Theory 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. |
| title | Reflection Theory of Nichols Algebras over Coquasi-Hopf Algebras with Bijective Antipode |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2602.07946 |