Newton polytopes in cluster algebras and $τ$-tilting theory
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910018446557184 |
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| author | Cao, Peigen |
| author_facet | Cao, Peigen |
| contents | We prove that the cluster monomials in non-initial cluster variables are uniquely determined by the Newton polytopes of their $F$-polynomials for skew-symmetrizable cluster algebras. Accordingly, we prove that the $τ$-rigid modules and the left finite multi-semibricks in $τ$-tilting theory are uniquely determined by the Newton polytopes of these modules. The key tools used in the proofs are the left Bongartz completion, $F$-invariant and partial $F$-invariant in the context of cluster algebras and $τ$-tilting theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07929 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Newton polytopes in cluster algebras and $τ$-tilting theory Cao, Peigen Representation Theory Rings and Algebras 13F60, 16G20 We prove that the cluster monomials in non-initial cluster variables are uniquely determined by the Newton polytopes of their $F$-polynomials for skew-symmetrizable cluster algebras. Accordingly, we prove that the $τ$-rigid modules and the left finite multi-semibricks in $τ$-tilting theory are uniquely determined by the Newton polytopes of these modules. The key tools used in the proofs are the left Bongartz completion, $F$-invariant and partial $F$-invariant in the context of cluster algebras and $τ$-tilting theory. |
| title | Newton polytopes in cluster algebras and $τ$-tilting theory |
| topic | Representation Theory Rings and Algebras 13F60, 16G20 |
| url | https://arxiv.org/abs/2602.07929 |