Quantum cluster variables via canonical submodules
Fan Xu, Yutong Yu
TL;DR
This paper explores quantum cluster algebras derived from marked surfaces without punctures, expressing variables via canonical submodules and establishing their positivity.
Contribution
It introduces a novel expression of quantum cluster variables using canonical submodules and proves positivity for this class.
Findings
Quantum cluster variables are expressed through canonical submodules.
Positivity is established for the studied class of quantum cluster algebras.
Abstract
We study quantum cluster algebras from marked surfaces without punctures. We express the quantum cluster variables in terms of the canonical submodules. As a byproduct, we obtain the positivity for this class of quantum cluster algebra.
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