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Original Articles

A Module-Theoretic Interpretation of Schiffler's Expansion Formula

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Pages 260-283 | Received 30 May 2011, Published online: 04 Jan 2013

REFERENCES

  • Amiot , C. ( 2009 ). Cluster categories for algebras of global dimension 2 and quivers with potential . Annales de l'Institut Fourier 59 : 2525 – 2590 .
  • Assem , I. , Brüstle , T. , Charbonneau-Jodoin , G. , Plamondon , P.-G. ( 2010 ). Gentle algebras arising from surface triangulations . J. Algebra and Number Theor. 4 : 201 – 229 .
  • Butler , M. C. R. , Ringel , C. M. ( 1987 ). Auslander-Reiten sequences with few middle terms . Comm. in Algebra 15 : 145 – 179 .
  • Brüstle , T. , Zhang , J. ( 2011 ). On the cluster category of a marked surface without punctures . J. Algebra and Number Theor. 5–4 : 529 – 566 .
  • Caldero , P. , Chapoton , F. ( 2006 ). Cluster algebras as Hall algebras of quiver representations . Comment. Math. Helv. 81 : 595 – 616 .
  • Caldero , P. , Chapoton , F. , Schiffler , R. ( 2006 ). Quivers with relations arising from clusters (A n case) . Trans. Amer. Math. Soc. 358 : 1347 – 1364 .
  • Dupont , G. , Thomas , H. Atomic bases in cluster algebras of type A and . http://arXiv.org/abs/1106.3758.
  • Derksen , H. , Weyman , J. , Zelevinsky , A. ( 2008 ). Quivers with potentials and their representations I: Mutations . Selecta Math. New Series 14 : 59 – 119 .
  • Fomin , S. , Shapiro , M. , Thurston , D. ( 2008 ). Cluster algebras and triangulated surfaces. Part I: Cluster complexes . Acta Mathematica 201 : 83 – 146 .
  • Fomin , S. , Zelevinsky , A. ( 2002 ). Cluster algebras. I. Foundations . J. Amer. Math. Soc. 15 : 497 – 529 .
  • Fomin , S. , Zelevinsky , A. ( 2007 ). Cluster algebras. IV: Coefficients . Compos. Math. Soc. 143 : 112 – 164 .
  • Fu , C. J. , Keller , B. ( 2010 ). On cluster algebras with coefficients and 2-Calabi-Yau categories . Trans. Amer. Math. Soc. 362 : 859 – 895 .
  • Keller , B. , Reiten , I. ( 2007 ). Cluster-tilted algebras are Gorenstein and stably Calabi-Yau . Adv. Math. 211 : 123 – 151 .
  • Keller , B. , Yang , D. ( 2011 ). Quiver mutation and derived equivalences . Adv. Math. 26 : 2118 – 2168 .
  • Koenig , S. , Zhu , B. ( 2008 ). From triangulated categories to abelian categories–cluster tilting in a general framework . Mathematische Zeitschrift 258 : 143 – 160 .
  • Labardini-Fragoso , D. ( 2009 ). Quivers with potentials associated to triangulated surfaces . Proc. London Math. Soc. 98 : 797 – 839 .
  • Palu , Y. ( 2008 ). Cluster characters for 2-Calabi-Yau triangulated categories . Annales de l'institut Fourier 58 : 2221 – 2248 .
  • Haupt , N. ( 2012 ). Euler characteristic of quiver Grassmannians and Ringel-Hall algebras of string algebras . Algebra and Representation Theory 15 : 755 – 793 .
  • Schiffler , R. ( 2010 ). On cluster algebras arising from unpunctured surfaces II . Adv. Math. 223 : 1885 – 1923 .
  • Schiffler , R. , Thomas , H. ( 2009 ). On cluster algebras arising from unpunctured surfaces . Int. Math. Res. Not. 17 : 3160 – 3189 .
  • Communicated by D. Zacharia.

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