Frobenius--Perron dimension via $τ$-tilting theory
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915160044601344 |
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| author | Adachi, Takahide Kase, Ryoichi |
| author_facet | Adachi, Takahide Kase, Ryoichi |
| contents | From the perspective of $τ$-tilting theory, we study Frobenius--Perron dimensions of finite-dimensional algebras. First, we evaluate the Frobenius--Perron dimensions of $τ$-tilting finite algebras by a combinatorial method in $τ$-tilting theory. Secondly, we give the upper bound for the Frobenius--Perron dimension for $τ$-tilting finite algebras of tame representation type. Thirdly, we determine the Frobenius--Perron dimensions of Nakayama algebras and generalized preprojective algebras of Dynkin type in the sense of Geiss--Leclerc--Schröer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05045 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frobenius--Perron dimension via $τ$-tilting theory Adachi, Takahide Kase, Ryoichi Representation Theory Combinatorics From the perspective of $τ$-tilting theory, we study Frobenius--Perron dimensions of finite-dimensional algebras. First, we evaluate the Frobenius--Perron dimensions of $τ$-tilting finite algebras by a combinatorial method in $τ$-tilting theory. Secondly, we give the upper bound for the Frobenius--Perron dimension for $τ$-tilting finite algebras of tame representation type. Thirdly, we determine the Frobenius--Perron dimensions of Nakayama algebras and generalized preprojective algebras of Dynkin type in the sense of Geiss--Leclerc--Schröer. |
| title | Frobenius--Perron dimension via $τ$-tilting theory |
| topic | Representation Theory Combinatorics |
| url | https://arxiv.org/abs/2501.05045 |