Serre cyclotomic algebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915692214747136 |
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| author | Pfeifer, Calvin |
| author_facet | Pfeifer, Calvin |
| contents | We introduce a class of proper differential graded algebras which we call Serre cyclotomic. They generalize fractionally Calabi-Yau algebras and categorify de la Peña's algebras of cyclotomic type. Path algebras of affine type and (higher) canonical algebras are examples of Serre cyclotomic algebras. Our definition is related to Elias-Hogancamp's theory of categorical diagonalization. We compute the categorical entropy of their Serre functors, in the sense of Dimitrov-Haiden-Katzarkov-Kontsevich, and use this to determine which graded path algebras and which homologically smooth graded gentle algebras are Serre cyclotomic. Finally, we show that trivial extension algebras of Serre cyclotomic algebras have finite global complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19873 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Serre cyclotomic algebras Pfeifer, Calvin Representation Theory We introduce a class of proper differential graded algebras which we call Serre cyclotomic. They generalize fractionally Calabi-Yau algebras and categorify de la Peña's algebras of cyclotomic type. Path algebras of affine type and (higher) canonical algebras are examples of Serre cyclotomic algebras. Our definition is related to Elias-Hogancamp's theory of categorical diagonalization. We compute the categorical entropy of their Serre functors, in the sense of Dimitrov-Haiden-Katzarkov-Kontsevich, and use this to determine which graded path algebras and which homologically smooth graded gentle algebras are Serre cyclotomic. Finally, we show that trivial extension algebras of Serre cyclotomic algebras have finite global complexity. |
| title | Serre cyclotomic algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2512.19873 |