On positivity for generalized cluster variables of affine quivers
Xueqing Chen, Ming Ding, Fan Xu
TL;DR
This paper proves the positivity of regular generalized cluster variables in affine quivers, extending positivity results to a broader class of cluster variables and constructing positive bases.
Contribution
It establishes positivity for regular generalized cluster variables in affine quivers, generalizing previous results and enabling the construction of positive bases.
Findings
Regular generalized cluster variables in affine quivers are positive.
Generalized cluster variables of affine quivers are positive.
Constructed various positive bases for affine quivers.
Abstract
It has been proved in \cite{LS} that cluster variables in cluster algebras of every skew-symmetric cluster algebra are positive. We prove that any regular generalized cluster variable of an affine quiver is positive. As a corollary, we obtain that generalized cluster variables of affine quivers are positive and construct various positive bases. This generalizes the results in \cite{Dupont} and \cite{DXX}.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Combinatorial Mathematics