Geodesic
Positivity and tameness in rank 2 cluster algebras
Journal of Algebraic Combinatorics, Tome 40 (2014) no. 3, pp. 823-840.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We study the relationship between the positivity property in a rank 2 cluster algebra, and the property of such an algebra to be tame. More precisely, we show that a rank 2 cluster algebra has a basis of indecomposable positive elements if and only if it is of finite or affine type. This statement disagrees with a conjecture by Fock and Goncharov.
Classification : 13F60
Keywords: cluster algebras, positivity, tameness 
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     title = {Positivity and tameness in rank 2 cluster algebras},
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Lee, Kyungyong; Li, Li; Zelevinsky, Andrei. Positivity and tameness in rank 2 cluster algebras. Journal of Algebraic Combinatorics, Tome 40 (2014) no. 3, pp. 823-840. http://geodesic.mathdoc.fr/item/JAC_2014__40_3_a2/