Generalized cluster algebras are subquotients of cluster algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866908364143853568 |
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| author | Ramos, Rolando Whiting, David |
| author_facet | Ramos, Rolando Whiting, David |
| contents | Generalized Cluster Algebras (GCA) are generalizations of Cluster Algebras (CA) with higher-order exchange relations. Previously, Chekhov-Shapiro conjectured that every GCA can be embedded into a CA. In this paper, we prove a modified version of this conjecture by providing a construction that realizes a given GCA as subquotient of some CA, as an algebra over the ground ring of the GCA via restriction of scalars. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20931 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized cluster algebras are subquotients of cluster algebras Ramos, Rolando Whiting, David Rings and Algebras Commutative Algebra 13F60 Generalized Cluster Algebras (GCA) are generalizations of Cluster Algebras (CA) with higher-order exchange relations. Previously, Chekhov-Shapiro conjectured that every GCA can be embedded into a CA. In this paper, we prove a modified version of this conjecture by providing a construction that realizes a given GCA as subquotient of some CA, as an algebra over the ground ring of the GCA via restriction of scalars. |
| title | Generalized cluster algebras are subquotients of cluster algebras |
| topic | Rings and Algebras Commutative Algebra 13F60 |
| url | https://arxiv.org/abs/2504.20931 |