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A remark on positivity for regular cluster variables of type $widetilde{D}_4$
DING Ming * #
School of Mathematical Sciences, Nankai University, Tianjin 300071
*Correspondence author
#Submitted by
Subject:
Funding: Specialized Research Fund for the Doctoral Program of Higher Education of China （No.20130031120004）
Opened online:22 February 2017
Accepted by: none
Citation: DING Ming.A remark on positivity for regular cluster variables of type $widetilde{D}_4$[OL]. [22 February 2017] http://en.paper.edu.cn/en_releasepaper/content/4719151
 
 
Inspired by Dupont's work, we show that the positivity for regular clustervariables of affine types can bededuced from the positivity for the interior of the regular cluster variablesassociated to quasi-simple modules in homogeneous tubes. Using this, we obtain an alternative proof of the positivity for regular clustervariables of type $widetilde{D}_{4}$.
Keywords:cluster variable, cluster algebra, cluster-tilting object, positivity.
 
 
 

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