On Indecomposable Exceptional Modules Over Gentle Algebras

REFERENCES

• Amiot , C. ( 2009 ). Cluster categories for algebras of global dimension 2 and quivers with potential . Annales de l'Institut Fourier 59 : 2525 – 2590 .
   Web of Science ®Google Scholar
• Assem , I. , Brüstle , T. , Charbonneau-Jodoin , G. , Plamondon , P.-G. ( 2010 ). Gentle algebras arising from surface triangulations . J. Algebra and Number Theory 4 : 201 – 229 .
   Web of Science ®Google Scholar
• Assem , I. , Dupont , G. ( 1987 ). Moduls over cluster-tilted algebras determined by their dimension vectors. Availabel at http://arxiv.org/abs/1202.5698 .
   Google Scholar
• Assem , I. , Skowroński , A. ( 1987 ). Iterated tilted algebras of type . Math. Z. 195 : 269 – 290 .
   Web of Science ®Google Scholar
• Buan , A. B. , Marsh , R. , Reineke , M. , Reiten , I. , Todorov , G. ( 2006 ). Tilting theory and cluster combinatorics . Adv. Math. 204 : 572 – 612 .
   Web of Science ®Google Scholar
• Butler , M. C. R. , Ringel , C. M. ( 1987 ). Auslander–Reiten sequences with few middle terms . Comm. in Algebra 15 : 145 – 179 .
   Web of Science ®Google Scholar
• Brüstle , T. , Zhang , J. ( 2011 ). On the cluster category of a marked surface without punctures. J. Algebra and Number Theory 5–4:529–566 .
   Google Scholar
• Carroll , A. T. Generic Modules for string algebras. http://arxiv.org/abs/1111.5064.
   Google Scholar
• Crawley-Boevey , W. W. ( 1989 ). Maps between representations of zero-relation algebras J. Algebra 126(2):259–263 .
   Google Scholar
• Derksen , H. , Weyman , J. , Zelevinsky , A. (2008). Quivers with potentials and their representations I: Mutations. Selecta Math., New Series 14:59–119.
   Web of Science ®Google Scholar
• Fomin , S. , Shapiro , M. , Thurston , D. ( 2008 ). Cluster algebras and triangulated surfaces. Part I: Cluster complexes . Acta Mathematica 201 : 83 – 146 .
   Web of Science ®Google Scholar
• Fomin , S. , Zelevinsky , A. ( 2002 ). Cluster algebras I. Foundations. J. Amer. Math. Soc. 15(2):497–529 (electronic) .
   Google Scholar
• Gabriel , P. ( 1972 ). Unzerlegbare Darstellungen. I. Manuscripta Math. 6:71–103; correction, ibid. 6:309 .
   Google Scholar
• Geng , S. F. , Peng , L. G. ( 2012 ). The dimension vectors of indecomposable modules of cluster-tilted algebras and the Fomin-Zelevinsky denominators conjecture . Acta Mathematica Sinica, English Series 28 ( 3 ): 581 – 586 .
   Web of Science ®Google Scholar
• Keller , B. ( 2010 ). Cluster algebras, quiver representations and triangulated categories. In: Triangulated Categories. LMS Lecture Notes Ser., Vol. 375. Cambrdge: Cambridge Univ. Press, pp. 76–160 .
   Google Scholar
• Mosher , L. ( 1983 ). Pseudo-Anosovs on punctured surfaces. Ph.D. thesis, Princeton University .
   Google Scholar
• Labardini-Fragoso , D. ( 2009 ). Quivers with potentials associated to triangulated surfaces . Proc. London Math. Soc. 98 : 797 – 839 .
   Web of Science ®Google Scholar
• Schröer , J. ( 1999 ). Modules without self-extensions over gentle algebras . J. Algebra 216 : 178 – 189 .
   Web of Science ®Google Scholar
• Schröer , J. , Zimmermann , A. ( 2003 ). Stable endomorphism algebras of modules over special biserial algebras . Math. Z 244 : 515 – 530 .
   Web of Science ®Google Scholar
• Thurston , D. Geometric intersection of curves on surfaces. Preprint http://www.math. columbia.edu/ᵭpt/DehnCoordinates.pdf
   Google Scholar
• Wald , B. , Waschbüsch , J. ( 1985 ). Tame biserial algebras . J. Algebra 95 ( 2 ): 480 – 500 .
   Web of Science ®Google Scholar
• Zhou , G. D. ( 2007 ). Algèbres courtoises et blocs à défaut dihédral. Ph.D thesis, Université de Picardie .
   Google Scholar
• Communicated by D. Zacharia.
   Google Scholar
• Color versions of one or more of the figures in the articlecan be found online at www.tandfonline.com/lagb.
   Google Scholar