Newton polytopes in cluster algebras and $\tau$-tilting theory
Representation Theory
2026-02-12 v2 Rings and Algebras
Abstract
We prove that the cluster monomials in non-initial cluster variables are uniquely determined by the Newton polytopes of their -polynomials for skew-symmetrizable cluster algebras. Accordingly, we prove that the -rigid modules and the left finite multi-semibricks in -tilting theory are uniquely determined by the Newton polytopes of these modules. The key tools used in the proofs are the left Bongartz completion, -invariant and partial -invariant in the context of cluster algebras and -tilting theory.
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Cite
@article{arxiv.2602.07929,
title = {Newton polytopes in cluster algebras and $\tau$-tilting theory},
author = {Peigen Cao},
journal= {arXiv preprint arXiv:2602.07929},
year = {2026}
}
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21 pages