Auslander–Reiten Triangles on Gorenstein Derived Categories

REFERENCES

• Amiot , C. ( 2009 ). Cluster categories for algebras of global dimensional 2 and quivers with potential . Ann. Inst. Fourier 59 : 2525 – 2590 .
   Web of Science ®Google Scholar
• Auslander , M. , Buchweitz , R. O. ( 1989 ). The homological theory of maximal Cohen-Macaulay approximations . Mem. Soc. Math. France 38 : 5 – 37 .
   Google Scholar
• Auslander , M. , Reiten , I. ( 1991 ). Applications of contravariantly finite subcategories . Adv. Math. 86 : 111 – 152 .
   Web of Science ®Google Scholar
• Auslander , M. , Reiten , I. , Smaløot , S. O. ( 1995 ). Representation Theory of Artin Algebras. Cambridge Studies in Adv. Math. 36., Cambridge University Press .
   Google Scholar
• Avramov , L. L. ( 2002 ). A. Martsinkovsky, Absolute, relative, and Tate cohomology of modules of finite Gorenstein dimension . Proc. London Math. Soc. 85 ( 3 ): 393 – 440 .
   Web of Science ®Google Scholar
• Beligiannis , A. ( 2005 ). Cohen-Macaulay modules, (co)torsion pairs and virtually Gorenstein algebras . J. Algebra 288 ( 1 ): 137 – 211 .
   Web of Science ®Google Scholar
• Beligiannis , A. ( 2011 ). On algebras of finite Cohen-Macaulay type . Adv. Math. 226 ( 2 ): 1973 – 2019 .
   Web of Science ®Google Scholar
• Bruns , W. , Herzog , J. ( 1998 ). Cohen-Macaulay Rings . Revised edition. Cambridge Studies in Adv. Math. 39. Cambridge : Cambridge University Press .
   Google Scholar
• Chen , X. W. ( 2008 ). An Auslander-type result for Gorenstein-projective modules . Adv. Math. 218 : 2043 – 2050 .
   Web of Science ®Google Scholar
• Christensen , L. W. ( 2000 ). Gorenstein Dimensions . Lecture Notes in Math. 1747. Berlin-New York : Springer-Verlag .
   Google Scholar
• Christensen , L. W. , Frankild , A. , Holm , H. ( 2006 ). On Gorenstein projective, injective and flat dimensions-a functorial description with applications . J. Algebra 302 ( 1 ): 231 – 279 .
   Web of Science ®Google Scholar
• Enochs , E. E. , Jenda , O. M. G. ( 1995 ). Gorenstein injective and projective modules . Math. Z. 220 ( 4 ): 611 – 633 .
   Web of Science ®Google Scholar
• Enochs , E. E. , Jenda , O. M. G. ( 2000 ). Relative Homological Algebra . De Gruyter Exp. Math. 30 . New York : Walter De Gruyter Co .
   Google Scholar
• Gao , N. ( 2010 ). Stable t-structures and Homotopy category of Gorenstein-projective modules . J. Algebra 324 : 2503 – 2511 .
   Web of Science ®Google Scholar
• Gao , N. , Zhang , P. ( 2010 ). Gorenstein derived categories . J. Algebra 323 ( 7 ): 2041 – 2057 .
   Web of Science ®Google Scholar
• Happel , D. ( 1991 ). On Gorenstein algebras. In: Representation Theory of Finite Groups and Finite-Dimensional Algebras. Prog. Math. Basel: Birkhüser, Vol. 95 , pp. 389 – 404 .
   Google Scholar
• Happel , D. ( 1988 ). Triangulated Categories in Representation Theory of Finite Dimensional Algebras . Cambridge : Cambridge University Press .
   Google Scholar
• Holm , H. ( 2004 ). Gorenstein homological dimensions . J. Pure Appl. Algebra 189 ( 1–3 ): 167 – 193 .
   Web of Science ®Google Scholar
• Hu , W. , Xi , C. C. ( 2010 ). Derived equivalences and stable equivalences of Morita type I . Nagoya Math. J. 200 : 107 – 152 .
   Web of Science ®Google Scholar
• Jøotrgensen , P. ( 2007 ). Existence of Gorenstein projective resolutions and Tate cohomology . J. Eur. Math. Soc. 9 : 59 – 76 .
   Web of Science ®Google Scholar
• Krause , H. ( 2000 ). Auslander-Reiten theory via Brown representability . K-Theory 20 ( 4 ): 331 – 344 .
   Google Scholar
• Li , Z. W. , Zhang , P. ( 2010 ). Gorenstein algebras of finite Cohen-Macaulay type . Adv. Math. 223 : 728 – 734 .
   Web of Science ®Google Scholar
• Ringel , C. M. ( 1984 ). Tame Algebras and Integral Quadratic Forms . Lecture Notes in Math. 1099 . Berlin-New York : Springer-Verlag .
   Google Scholar
• Verdier , J. L. ( 1977 ). Categories Derivees Etat O. Lecture Notes in Math. 569 . Berlin-New York : Springer-Verlag .
   Google Scholar
• Communicated by Q. Wu.
   Google Scholar