Positivity for Regular Cluster Characters in Acyclic Cluster Algebras

G. Dupont

Positivity for Regular Cluster Characters in Acyclic Cluster Algebras

Representation Theory 2011-09-16 v2 Rings and Algebras

Authors: G. Dupont

Abstract

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.

Keywords

cluster algebra acyclic quiver regular module cluster character positivity indecomposable module

Cite

@article{arxiv.0911.0714,
  title  = {Positivity for Regular Cluster Characters in Acyclic Cluster Algebras},
  author = {G. Dupont},
  journal= {arXiv preprint arXiv:0911.0714},
  year   = {2011}
}

Comments

v2 : 15 pages. Title changed. The paper was entirely rewritten and shortened. For the sake of simplicity, the context was reduced to acyclic cluster algebras and the section on the A-double-infinite quiver was removed. Nevertheless, the methods and the results remain essentially unchanged. To appear in the Journal of Algebra and its Applications

Positivity for Regular Cluster Characters in Acyclic Cluster Algebras

Abstract

Keywords

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