REFERENCES
- Assem , I. , Simson , D. , Skowroński , A. ( 2006 ). Elements of the representation theory of associative algebras, volumn 1: techniques of representation theory . London Math. Soc. Student Texts 65 , Cambridge : Cambridge University Press .
- Auslander , M. , Reiten , I. , Smalø , S. O. ( 1995 ). Representation Theory of Artin Algebras . Cambridge : Cambridge University Press .
- Barot , M. , Kussin , D. , Lenzing , H. ( 2008 ). The Grothendieck group of a cluster category . J. Pure Appl. Algebra 212 ( 1 ): 33 – 46 .
- Beaudet , L. , Brüstle , T. , Todorov , G. ( 2011 ) Projective dimension of modules over cluster-tilted algebras. Preprint, arXiv:1111.2013v1 .
- Bongartz , K. ( 1981 ). Tilted algebras. Representations of algebras (Puebla, 1980), Lecture Notes in Math. 903 , Berlin-New York : Springer , pp. 26 – 38 .
- Buan , A. B. , Iyama , O. , Reiten , I. , Scott , J. (2009). Cluster structure for 2-Calabi-Yau categories and unipotent groups. Compos. Math. 145(4): 1035–1079
- Buan , A. B. , Marsh , R. J. , Reiten , I. ( 2007 ). Cluster-tilted algebras . Trans. Amer. Math. Soc. 359 ( 1 ): 323 – 332 .
- Buan , A. B. , Marsh , R. J. , Vatne , D. F. ( 2010 ). Cluster structure from 2-Calabi-Yau categories with loops . Math. Z. 265 ( 4 ): 951 – 970 .
- Burban , I. , Iyama , O. , Keller , B. , Reiten , I. ( 2008 ). Cluster tilting for one-dimensional hypersurface singularities . Adv. Math. 217 ( 6 ): 2443 – 2484 .
- Fu , C. , Liu , P. ( 2009 ). Lifting to cluster-tilting objects in 2-Calabi-Yau triangulated categories . Comm. Algebra 37 : 1 – 9 .
- Happel , D. ( 1988 ). Triangulated categories in the representation theory of finite dimensional algebras . London Math. Soc. Lecture Note Ser. 119, London-New York : Cambridge University Press .
- Happel , D. ( 1992 ). Partial tilting modules and recollement, in “Proceedings, Malcev Conference” , Contemporary Mathematics 131, Providence: pp. 345 – 361
- Happel , D. , Ringel , C. M. ( 1982 ). Tilted algebras . Trans. Amer. Math. Soc. 274 ( 2 ): 399 – 443
- Happel , D. , Unger , L. ( 1989 ). Almost complete tilting modules . Proc. Amer. Math. Soc. 107 : 603 – 610 .
- Holm , T. , Jørgensen , P. ( 2010 ). On the relation between cluster and classical tilting . J. Pure Appl. Algebra 214 ( 9 ): 1523 – 1533 .
- Iyama , O. , Yoshino , Y. ( 2008 ). Mutation in triangulated categories and rigid Cohen-Macaulay modules . Inv. Math. 172 ( 1 ): 117 – 168 .
- Keller , B. ( 2010 ). Cluster algebras, quiver representations and triangulated categories , in Triangulated Categories (edited by Holm , T. , Jøgensen , P. , Rouquier , R. ). London Math. Soc. Lecture Note Ser. 375 , Cambridge : Cambridge University Press .
- Keller , B. , Reiten , I. ( 2007 ). Cluster-tilted algebras are Gorenstein and stably Calabi–Yau . Adv. Math. 211 ( 1 ): 123 – 151 .
- Koenig , S. , Zhu , B. ( 2008 ). From triangulated categories to abelian categories-cluster tilting in a general framework . Math. Z. 258 : 143 – 160 .
- Liu , P. ( 2010 ). Exchange relation for 2-Calabi-Yau tilted algebras (in Chinese) . Sci. Sin. Math. 40 ( 11 ): 1039 – 1044 .
- Liu , P. , Xie , Y. ( 2013 ). Lifting to maximal rigid objects in 2-Calabi-Yau triangulated categories . Proc. Amer. Math. Soc. 141 : 3361 – 3367 .
- Reiten , I. ( 2011 ). Cluster categories . Proceedings of the International Congress of Mathematicians 2010 (ICM 2010) , vol. 1 , New Delhi : Hindustan Book Agency , pp. 558 – 594 .
- Riedtmann , C. , Schofield , A. ( 1991 ). On a simplicial complex associated with tilting modules . Comment. Math. Helv. 66 : 70 – 78 .
- Ringel , C. M. ( 2006 ). Some remarks concerning tilting modules and tilted algebras. Origin. Relevance. Future . An appendix to the Handbook of Tilting Theory (edited by Angeleri-Huegel , L. , Happel , D. , Krause , H. ). London Mathematical Society Lecture Notes Series 332, Cambridge : Cambridge University Press .
- Smith , D. ( 2008 ). On tilting modules over cluster-tilted algebras . Illinois J. Math. 52 ( 4 ): 1223 – 1247 .
- Vatne , D. F. ( 2011 ). Endomorphism rings of maximal rigid objects in cluster tubes . Colloq. Math. 123 : 63 – 93 .
- Yang , D. ( 2012 ). Endomorphism algebras of maximal rigid objects in cluster tubes . Comm. Algebra 40 : 4347 – 4371 .
- Zhou , Y. , Zhu , B. ( 2011 ). Maximal rigid subcategories in 2-Calabi-Yau triangulated categories . J. Algebra 348 : 49 – 60 .
- Communicated by Q. Wu.