منابع مشابه
Cluster algebras arising from cluster tubes
We study the cluster algebras arising from cluster tubes with rank bigger than 1. Cluster tubes are 2−Calabi-Yau triangulated categories which contain no cluster tilting objects, but maximal rigid objects. Fix a maximal rigid object T in the cluster tube Γn of rank n (n > 1). For any indecomposable rigid object M in Γn, we define an analogous XM of Caldero-Chapton’s formula (or Palu’s cluster c...
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We study cluster algebras with principal and arbitrary coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of certain paths on a triangulation of the surface. As an immediate consequence, we prove the positivity conjecture of Fomin and Zelevinsky for these cluster a...
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These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generator...
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ژورنال
عنوان ژورنال: International Electronic Journal of Algebra
سال: 2016
ISSN: 1306-6048
DOI: 10.24330/ieja.266199