Irreducible representations of pointed Hopf algebras of type $A_2$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915416991858688 |
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| author | Iglesias, Agustín García Rodriguez, Alfio Antonio |
| author_facet | Iglesias, Agustín García Rodriguez, Alfio Antonio |
| contents | We classify the irreducible representations of a family of finite-dimensional pointed liftings $H_λ$ of the Nichols algebra associated with the diagram $A_2$ with parameter $q=-1$. We show that these algebras have infinite representation type and construct an indecomposable $H_λ$-module of dimension $n$ for each $n\in\mathbb{N}$. Finally, we study a semisimple category $\underline{\operatorname{Rep}} H_λ$ arising as a quotient of $\operatorname{Rep} H_λ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21978 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Irreducible representations of pointed Hopf algebras of type $A_2$ Iglesias, Agustín García Rodriguez, Alfio Antonio Quantum Algebra Representation Theory 16T05 We classify the irreducible representations of a family of finite-dimensional pointed liftings $H_λ$ of the Nichols algebra associated with the diagram $A_2$ with parameter $q=-1$. We show that these algebras have infinite representation type and construct an indecomposable $H_λ$-module of dimension $n$ for each $n\in\mathbb{N}$. Finally, we study a semisimple category $\underline{\operatorname{Rep}} H_λ$ arising as a quotient of $\operatorname{Rep} H_λ$. |
| title | Irreducible representations of pointed Hopf algebras of type $A_2$ |
| topic | Quantum Algebra Representation Theory 16T05 |
| url | https://arxiv.org/abs/2507.21978 |