Relation between generalized and ordinary cluster algebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915719583629312 |
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| author | Akagi, Ryota Nakanishi, Tomoki |
| author_facet | Akagi, Ryota Nakanishi, Tomoki |
| contents | Recently, Ramos and Whiting showed that any generalized cluster algebra of geometric type is isomorphic to a quotient of a subalgebra of a certain cluster algebra. Based on their idea and method, we show that the same property holds for any generalized cluster algebra with $y$-variables in an arbitrary semifield. We also present the relations between the $C$-matrices, the $G$-matrices, and the $F$-polynomials of a generalized cluster pattern and those of the corresponding composite cluster pattern. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21062 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relation between generalized and ordinary cluster algebras Akagi, Ryota Nakanishi, Tomoki Representation Theory Commutative Algebra Recently, Ramos and Whiting showed that any generalized cluster algebra of geometric type is isomorphic to a quotient of a subalgebra of a certain cluster algebra. Based on their idea and method, we show that the same property holds for any generalized cluster algebra with $y$-variables in an arbitrary semifield. We also present the relations between the $C$-matrices, the $G$-matrices, and the $F$-polynomials of a generalized cluster pattern and those of the corresponding composite cluster pattern. |
| title | Relation between generalized and ordinary cluster algebras |
| topic | Representation Theory Commutative Algebra |
| url | https://arxiv.org/abs/2512.21062 |