Super Caldero--Chapoton map for type $A$
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914700549160960 |
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| author | Çanakçı, İlke Fedele, Francesca Elsener, Ana Garcia Serhiyenko, Khrystyna |
| author_facet | Çanakçı, İlke Fedele, Francesca Elsener, Ana Garcia Serhiyenko, Khrystyna |
| contents | One can explicitly compute the generators of a surface cluster algebra either combinatorially, through dimer covers of snake graphs, or homologically, through the CC-map applied to indecomposable modules over the appropriate algebra. Recent work by Musiker, Ovenhouse and Zhang used Penner and Zeitlin's decorated super Teichm{ü}ller theory to define a super version of the cluster algebra of type $A$ and gave a combinatorial formula to compute the even generators. We extend this theory by giving a homological way of explicitly computing these generators by defining a super CC-map for type $A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15495 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Super Caldero--Chapoton map for type $A$ Çanakçı, İlke Fedele, Francesca Elsener, Ana Garcia Serhiyenko, Khrystyna Representation Theory Combinatorics Rings and Algebras 13F60, 17A70, 16G10, 30F60 One can explicitly compute the generators of a surface cluster algebra either combinatorially, through dimer covers of snake graphs, or homologically, through the CC-map applied to indecomposable modules over the appropriate algebra. Recent work by Musiker, Ovenhouse and Zhang used Penner and Zeitlin's decorated super Teichm{ü}ller theory to define a super version of the cluster algebra of type $A$ and gave a combinatorial formula to compute the even generators. We extend this theory by giving a homological way of explicitly computing these generators by defining a super CC-map for type $A$. |
| title | Super Caldero--Chapoton map for type $A$ |
| topic | Representation Theory Combinatorics Rings and Algebras 13F60, 17A70, 16G10, 30F60 |
| url | https://arxiv.org/abs/2402.15495 |