Denominator vectors and dimension vectors from triangulated surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909296143368192 |
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| author | Yurikusa, Toshiya |
| author_facet | Yurikusa, Toshiya |
| contents | In a categorification of skew-symmetric cluster algebras, each cluster variable corresponds with an indecomposable module over the associated Jacobian algebra. Buan, Marsh and Reiten studied when the denominator vector of each cluster variable in an acyclic cluster algebra coincides with the dimension vector of the corresponding module. In this paper, we give analogues of their results for cluster algebras from triangulated surfaces by comparing two kinds of intersection numbers of tagged arcs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_08097 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Denominator vectors and dimension vectors from triangulated surfaces Yurikusa, Toshiya Combinatorics Representation Theory 13F60, 16G20 In a categorification of skew-symmetric cluster algebras, each cluster variable corresponds with an indecomposable module over the associated Jacobian algebra. Buan, Marsh and Reiten studied when the denominator vector of each cluster variable in an acyclic cluster algebra coincides with the dimension vector of the corresponding module. In this paper, we give analogues of their results for cluster algebras from triangulated surfaces by comparing two kinds of intersection numbers of tagged arcs. |
| title | Denominator vectors and dimension vectors from triangulated surfaces |
| topic | Combinatorics Representation Theory 13F60, 16G20 |
| url | https://arxiv.org/abs/2305.08097 |