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Original Articles

Cluster-Tilted Algebras of Type Dn

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Pages 2418-2432 | Received 19 Feb 2009, Published online: 17 Jun 2010

REFERENCES

  • Auslander , M. , Reiten , I. , Smalφ , S. O. ( 1995 ). Representation Theory of Artin Algebras . Cambridge Studies in Advanced Math. 36 . Cambridge : Cambridge Univ. Press .
  • Assem , I. , Simson , D. , Skowronski , A. ( 2006 ). Elements of the Representation Theory of Associative Algebras . Vol. 1 . London Math. Soc. Student Texas 65. Cambridge : Cambridge University Press .
  • Buan , A. , Marsh , R. , Reiten , I. ( 2007 ). Cluster-tilted algebra . Trans. Amer. Math. Soc. 359 : 323 – 332 .
  • Buan , A. , Marsh , R. , Reiten , I. ( 2006 ). Cluster-tilted algebra of finite representation type . J. Algebra 306 : 412 – 431 .
  • Buan , A. , Marsh , R. , Reineke , M. , Reiten , I. , Todorov , G. ( 2006 ). Tilting theory and cluster combinatorices . Adv. in Math. 204 : 572 – 618 .
  • Buan , A. , Torkildsen , H. ( 2009 ). The number of elements in the mutation class of a quiver of type D n . Electron. Combin. 16 ( 1 ): 1 – 23 .
  • Buan , A. , Vatne , D. ( 2008 ). Derived equivalence classification of cluster-tilted algebra of type A n . J. Algebra 319 : 2723 – 2738 .
  • Caldero , P. , Chapoton , F. , Schiffler , R. ( 2006 ). Quivers with relations arising from clusters (A n case) . Trans. Amer. Math. Soc. 358 : 1347 – 1364 .
  • Caldero , P. , Chapoton , F. , Schiffler , R. ( 2006 ). Quivers with relations and cluster-tilted algebras . Algebra Represention Theory 9 : 359 – 376 .
  • Fomin , S. , Zelevinsky , A. ( 2002 ). Cluster algebra I: Foundation . J. Amer. Math. Soc. 15 : 497 – 529 .
  • Fomin , S. , Zelevinsky , A. ( 2003 ). Cluster algebra II: Finite type classification . Invention Math. 154 : 63 – 121 .
  • Happel , D. ( 1988 ). Triangulated Categories in the Representation Theory of Finite Dimensional Algebras . London Math. Soc. Lecture Notes Series 119 . Cambridge : Cambridge Univ. Press .
  • Ringel , C. M. ( 1984 ). Tame Algebras and Integral Quadratic Forms . Lecture Notes in Math. 1099 . Heidelberg : Springer Verlag .
  • Seven , A. ( 2007 ). Recognizing cluster algebra of finite type . Electron. J. Combin. 14 : 1 – 35 .
  • Schiffler , R. ( 2008 ). A geometric model for cluster category of type D n . J. Algebra Comb. 27 ( 1 ): 1 – 21 .
  • Torkildsen , H. ( 2008 ). Counting cluster-tilted algebras of type A n . International Electronic J. Algebra 4 : 149 – 158 .
  • Vatne , D. ( 2010 ). The mutation class of D n quivers . Comm. Alg. 38 : 1137 – 1146 .
  • Communicated by Q. Wu.

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