Algebras in fusion categories: species and hereditary algebras
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914342349307904 |
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| author | Heng, Edmund Stroiński, Mateusz |
| author_facet | Heng, Edmund Stroiński, Mateusz |
| contents | We initiate the study of non-semisimple algebras in fusion categories by establishing the framework of $\mathcal{C}$-species -- analogous to the framework of species and quivers used in the study of Artin algebras. Under the (necessary) assumption that the fusion category is separable, we show that any algebra is Morita equivalent to an admissible quotient of the path algebra of a $\mathcal{C}$-species. Moreover, we show that an algebra is hereditary if and only if no further quotient is required. These results generalise that of Gabriel's for finite-dimensional algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19144 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Algebras in fusion categories: species and hereditary algebras Heng, Edmund Stroiński, Mateusz Representation Theory Category Theory Quantum Algebra Rings and Algebras 18M20, 18D25, 16G20 We initiate the study of non-semisimple algebras in fusion categories by establishing the framework of $\mathcal{C}$-species -- analogous to the framework of species and quivers used in the study of Artin algebras. Under the (necessary) assumption that the fusion category is separable, we show that any algebra is Morita equivalent to an admissible quotient of the path algebra of a $\mathcal{C}$-species. Moreover, we show that an algebra is hereditary if and only if no further quotient is required. These results generalise that of Gabriel's for finite-dimensional algebras. |
| title | Algebras in fusion categories: species and hereditary algebras |
| topic | Representation Theory Category Theory Quantum Algebra Rings and Algebras 18M20, 18D25, 16G20 |
| url | https://arxiv.org/abs/2602.19144 |