Acyclic cluster algebras with dense $g$-vector fans
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916370174705664 |
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| author | Yurikusa, Toshiya |
| author_facet | Yurikusa, Toshiya |
| contents | The $g$-vector fans play an important role in studying cluster algebras and silting theory. We survey cluster algebras with dense $g$-vector fans and show that a connected acyclic cluster algebra has a dense $g$-vector fan if and only if it is either finite type or affine type. As an application, we classify finite dimensional hereditary algebras with dense $g$-vector fans. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_13482 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Acyclic cluster algebras with dense $g$-vector fans Yurikusa, Toshiya Representation Theory Commutative Algebra 13F60, 05E45, 16G20 The $g$-vector fans play an important role in studying cluster algebras and silting theory. We survey cluster algebras with dense $g$-vector fans and show that a connected acyclic cluster algebra has a dense $g$-vector fan if and only if it is either finite type or affine type. As an application, we classify finite dimensional hereditary algebras with dense $g$-vector fans. |
| title | Acyclic cluster algebras with dense $g$-vector fans |
| topic | Representation Theory Commutative Algebra 13F60, 05E45, 16G20 |
| url | https://arxiv.org/abs/2107.13482 |