Friezes and a construction of the euclidean cluster variables

2010/02/28 by Assem, I., Dupont, G.
#13F60 #16G20 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1003.0197

Abstract

Let Q be an euclidean quiver. Using friezes in the sense of Assem-Reutenauer-Smith, we provide an algorithm for computing the (canonical) cluster character associated to any object in the cluster category of Q. In particular, this algorithm allows to compute all the cluster variables in the cluster algebra associated to Q. It also allows to compute the sum of the Euler characteristics of the quiver grassmannians of any module M over the path algebra of Q.

Related

• Friezes of type D
• Friezes of type D-tilde
• Cluster algebras as Hall algebras of quiver representations
• Friezes, Strings and Cluster Variables
• A ℤ-basis for the cluster algebra associated to an affine quiver