Caldero–Keller Approach to the Denominators of Cluster Variables

REFERENCES

• Buan , A. , Caldero , P. , Keller , B. , Marsh , R. , Reiten , I. , Todorov , G. ( 2007 ). Appendix to Cluster and seeds in acyclic cluster algebras . Proc. Amer. Math. Soc. 135 : 3049 – 3060 .
   Web of Science ®Google Scholar
• Buan , A. , Marsh , R. , Reineke , M. , Reiten , I. , Todorov , G. ( 2006 ). Tilting theory and cluster combinatorics . Advances in Mathematics 204 : 572 – 618 .
   Web of Science ®Google Scholar
• Buan , A. , Marsh , R. , Reiten , I. ( 2008 ). Cluster mutation via quiver representations . Commentarii Mathematici Helvetici 83 : 143 – 177 .
   Web of Science ®Google Scholar
• Buan , A. , Marsh , R. , Reiten , I. ( 2009 ). Denominators of cluster variables . J. Lond. Math. Soc. (2) 79 : 589 – 611 .
   Web of Science ®Google Scholar
• Buan , A. , Marsh , R. , Reiten , I. , Todorov , G. ( 2007 ). Clusters and seeds in acyclic cluster algebras . Proc. Amer. Math. Soc. 135 : 3049 – 3060 .
   Web of Science ®Google Scholar
• Caldero , P. , Chapoton , F. ( 2006 ). Cluster algebras as Hall algebras of quiver representations . Commentarii Mathematici Helvetici 81 : 596 – 616 .
   Google Scholar
• Caldero , P. , Chapoton , F. , Schiffler , R. ( 2006 ). Quivers with relations and cluster tilted algebras . Algebras and Representation Theory 9 : 359 – 376 .
   Web of Science ®Google Scholar
• Caldero , P. , Chapoton , F. , Schiffler , R. ( 2006 ). Quivers with relations arising from clusters (A n case) . Transactions of the AMS 358 : 1347 – 1354 .
   Web of Science ®Google Scholar
• Caldero , P. , Keller , B. ( 2006 ). From triangulated categories to cluster algebras II . Annales Scientifiques de l'Ecole Normale Supérieure 39 : 83 – 100 .
   Google Scholar
• Caldero , P. , Keller , B. ( 2008 ). From triangulated categories to cluster algebras . Inventiones Mathematicae 172 : 169 – 211 .
   Web of Science ®Google Scholar
• Fomin , S. , Zelevinsky , A. ( 2002 ). Cluster algebras I: Foundations . J. Amer. Math. Soc. 15 : 497 – 529 .
   Web of Science ®Google Scholar
• Fomin , S. , Zelevinsky , A. ( 2003 ). Cluster algebras II: Finite type classification . Inventiones Mathematicae 154 : 63 – 121 .
   Web of Science ®Google Scholar
• Happel , D. , Unger , L. ( 2005 ). On the set of tilting objects in hereditary categories . Fields Institute Communications 45 : 141 – 159 .
   Google Scholar
• Marsh , R. , Reineke , M. , Zelevinsky , A. ( 2003 ). Generalized associahedra via quiver representations . Trans. AMS 355 : 4171 – 4186 .
   Web of Science ®Google Scholar
• Palu , Y. ( 2003 ). Cluster characters for 2-Calabi–Yau triangulated categories . Ann. Inst. Fourier (Grenoble) 58 : 2221 – 2248 .
   Google Scholar
• Communicated by C. Cibils.
   Google Scholar