2009/11/04 by Grégoire Dupont, G. Dupont, Dupont, G.
Mathematics · #13F60 #16G20 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:13F60 #msc:16G20
paper · pdf · doi:10.48550/arxiv.0911.0714
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
openalex publication_date 2009/11/04 · arxiv created 2011/09/15 · arxiv updated 2011/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.