Positivity for Regular Cluster Characters in Acyclic Cluster Algebras
Positivity for Regular Cluster Characters in Acyclic Cluster Algebras
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DOI：
10.1142/s0219498812500697
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发表时间：
2009-11
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影响因子：
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通讯作者：
G. Dupont
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作者：
G. Dupont
设$Q$是一个非循环的群代数，$\mathcal A（Q）$是相应的簇代数。设H是代数闭域上Q的路代数，M是不可分解的正则H-模.我们证明了当$H$是驯服的且$M$是任意正则的$H$-模，或者$H$是野生的且$M$是非拟单的正则Schur模时，$M$在$\mathcal A（Q）$的初始种子中所表示的簇特征标的正性.
Let $Q$ be an acyclic quiver and let $\mathcal A(Q)$ be the corresponding cluster algebra. Let $H$ be the path algebra of $Q$ over an algebraically closed field and let $M$ be an indecomposable regular $H$-module. We prove the positivity of the cluster characters associated to $M$ expressed in the initial seed of $\mathcal A(Q)$ when either $H$ is tame and $M$ is any regular $H$-module, or $H$ is wild and $M$ is a regular Schur module which is not quasi-simple.