Classification of finite type fusion quivers
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916206413348864 |
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| author | Elias, Ben Heng, Edmund |
| author_facet | Elias, Ben Heng, Edmund |
| contents | In recent work, the second author introduced the concept of Coxeter quivers, generalizing several previous notions of a quiver representation. Finite type Coxeter quivers were classified, and their indecomposable objects were shown to be in bijection with positive roots, generalizing a classical theorem of Gabriel. In this paper we define fusion quivers, a natural generalization of Coxeter quivers. We classify the finite type fusion quivers, and prove the analogue of Gabriel's theorem. As a special case, this proves a generalised quantum McKay correspondence for fusion categories, an analogue of Auslander--Reiten's result for finite groups in the fusion categorical setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_09714 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of finite type fusion quivers Elias, Ben Heng, Edmund Representation Theory Quantum Algebra 16G20, 16D90, 18M20 In recent work, the second author introduced the concept of Coxeter quivers, generalizing several previous notions of a quiver representation. Finite type Coxeter quivers were classified, and their indecomposable objects were shown to be in bijection with positive roots, generalizing a classical theorem of Gabriel. In this paper we define fusion quivers, a natural generalization of Coxeter quivers. We classify the finite type fusion quivers, and prove the analogue of Gabriel's theorem. As a special case, this proves a generalised quantum McKay correspondence for fusion categories, an analogue of Auslander--Reiten's result for finite groups in the fusion categorical setting. |
| title | Classification of finite type fusion quivers |
| topic | Representation Theory Quantum Algebra 16G20, 16D90, 18M20 |
| url | https://arxiv.org/abs/2404.09714 |