On Partial Tilting Complexes

REFERENCES

• Abe , H. ( 2008 ). Noetherian algebras of finite selfinjective dimension . Comm. Algebra 36 : 493 – 507 .
   Web of Science ®Google Scholar
• Abe , H. , Hoshino , M. ( 2007 ). Derived equivalences and Gorenstein algebras . J. Pure Appl. Algebra 211 : 55 – 69 .
   Web of Science ®Google Scholar
• Auslander , M. , Platzeck , M. I. , Reiten , I. ( 1979 ). Coxeter functors without diagrams . Trans. Amer. Math. Soc. 250 : 1 – 46 .
   Web of Science ®Google Scholar
• Bass , H. ( 1960 ). Finitistic dimension and a homological generalization of semi-primary rings . Trans. Amer. Math. Soc. 95 : 466 – 488 .
   Google Scholar
• Bernstein , I. N. , Gelfand , I. M. , Ponomarev , V. A. ( 1973 ). Coxeter functors and Gabriel's theorem . Russian Math. Surveys 28 : 17 – 32 .
   Google Scholar
• Bökstedt , M. , Neeman , A. ( 1993 ). Homotopy limits in triangulated categories . Compositio Math. 86 : 209 – 234 .
   Web of Science ®Google Scholar
• Bongartz , K. ( 1981 ). Tilted algebras . In: Representations of Algebras (Puebla, 1980) . Lecture Notes in Math. , Vol. 903 . Berlin : Springer . pp. 26 – 38 .
   Google Scholar
• Brenner , S. , Butler , M. C. R. ( 1980 ). Generalization of the Bernstein-Gelfand-Ponomarev reflection functors . In: Representation Theory, II (Proc. Second Internat. Conf., Carleton Univ., Ottawa, Ont., 1979) . Lecture Notes in Math., Vol. 832 . Berlin : Springer , pp. 103 – 169 .
   Google Scholar
• Coelho , F. , Happel , D. , Unger , L. ( 1994 ). Complements to partial tilting modules . J. Algebra 170 : 184 – 205 .
   Web of Science ®Google Scholar
• Grothendieck , A. ( 1977 ). Groupes des classes des catègories abeliennes et triangulées. complexes parfaits . In: Seminaire de Geometrie Algebrique du Bois-Marie (SGA 5) . Lecture Notes in Math. , Vol. 589 . Berlin : Springer , pp. 351 – 371 .
   Google Scholar
• Happel , D. ( 1988 ). Triangulated Categories in the Representation Theory of Finite-Dimensional Algebra . London Math. Soc. Lecture Note Series , Vol. 119 . Cambridge : Cambridge Univ. Press .
   Google Scholar
• Happel , D. (1992). Partial tilting modules and recollement. Proceedings of the International Conference on Algebra, Part 2 (Novosibirsk, 1989), Contemp. Math., 131, Part 2. Providence, RI: Amer. Math. Soc. pp. 345–361.
   Google Scholar
• Happel , D. , Ringel , C. M. ( 1982 ). Tilted algebras . Trans. Amer. Math. Soc. 274 : 399 – 443 .
   Web of Science ®Google Scholar
• Happel , D. , Unger , L. ( 2005 ). On a partial order of tilting modules . Algebr. Represent. Theory 8 : 147 – 156 .
   Web of Science ®Google Scholar
• Hartshorne , R. ( 1966 ). Residues and Duality . In: Lecture Notes of a Seminar on the Work of A. Grothendieck, given at Harvard 1963/64 . Lecture Notes in Math. , Vol. 20 . Berlin : Springer .
   Google Scholar
• Hoshino , M. , Kato , Y. ( 2002 ). Tilting complexes defined by idempotents . Comm. Algebra 30 : 83 – 100 .
   Web of Science ®Google Scholar
• Keller , B. , Vossieck , D. ( 1988 ). Aisles in derived categories . Bull. Soc. Math. Belg. 40 : 239 – 253 .
   Google Scholar
• Matsumura , H. ( 1986 ). Commutative Ring Theory . Translated from the Japanese by M. Reid . Cambridge : Cambridge Univ. Press .
   Google Scholar
• Miyashita , Y. ( 1986 ). Tilting modules of finite projective dimension . Math. Z. 193 : 113 – 146 .
   Web of Science ®Google Scholar
• Rickard , J. ( 1989 ). Morita theory for derived categories . J. London Math. Soc. ( 2 ) 39 : 436 – 456 .
   Google Scholar
• Rickard , J. , Schofield , A. ( 1989 ). Cocovers and tilting modules . Math. Proc. Cambridge Philos. Soc. 106 : 1 – 5 .
   Web of Science ®Google Scholar
• Riedtmann C. Schofield , A. ( 1991 ). On a simplicial complex associated with tilting modules . Comment. Math. Helv. 66 : 70 – 78 .
   Google Scholar
• Verdier , J. L. ( 1977 ). Catégories dérivées, état 0 . In: Cohomologie étale . Lecture Notes in Math. , Vol. 569 . Berlin : Springer , pp. 262 – 311 .
   Google Scholar
• Communicated by D. Zacharia.
   Google Scholar