Lattice structure in cluster algebra of finite type and non-simply-laced Ingalls-Thomas bijection
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911991595008000 |
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| author | Gyoda, Yasuaki |
| author_facet | Gyoda, Yasuaki |
| contents | In this paper, we demonstrate that the lattice structure of a set of clusters in a cluster algebra of finite type is anti-isomorphic to the torsion lattice of a certain Geiss-Leclerc-Schröer (GLS) path algebra and to the $c$-Cambrian lattice. We prove this by explicitly describing the exchange quivers of cluster algebras of finite type. Specifically, we prove that these quivers are anti-isomorphic to those formed by support $τ$-tilting modules in GLS path algebras and to those formed by $c$-clusters consisting of almost positive roots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_08935 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Lattice structure in cluster algebra of finite type and non-simply-laced Ingalls-Thomas bijection Gyoda, Yasuaki Representation Theory Combinatorics 13F60, 16G20, 17B22 In this paper, we demonstrate that the lattice structure of a set of clusters in a cluster algebra of finite type is anti-isomorphic to the torsion lattice of a certain Geiss-Leclerc-Schröer (GLS) path algebra and to the $c$-Cambrian lattice. We prove this by explicitly describing the exchange quivers of cluster algebras of finite type. Specifically, we prove that these quivers are anti-isomorphic to those formed by support $τ$-tilting modules in GLS path algebras and to those formed by $c$-clusters consisting of almost positive roots. |
| title | Lattice structure in cluster algebra of finite type and non-simply-laced Ingalls-Thomas bijection |
| topic | Representation Theory Combinatorics 13F60, 16G20, 17B22 |
| url | https://arxiv.org/abs/2211.08935 |