Exceptional Pairs in Hereditary Categories

REFERENCES

• Baer , D. ( 1989 ). A note on wild quiver algebras and tilting modules . Commun. Algebra 17 ( 3 ): 751 – 757 .
   Web of Science ®Google Scholar
• Crawley-Boevey , W. ( 1993 ). Exceptional sequences of representations of quivers. Proceedings of ICRA VI, Carleton-Ottawa, CMS Conf. Proc. 14 , pp. 117 – 124 .
   Google Scholar
• Geigle , W. , Lenzing , H. ( 1987 ). A class of weighted projective curves arising in representation theory of finite dimensional algebras . In: Singularities, Representations of Algebras, and Vector Bundles . Springer Lecture Notes in Mathematics, 1273 . pp. 265 – 297 .
   Google Scholar
• Geigle , W. , Lenzing , H. ( 1991 ). Perpendicular categories with applications to representations and sheaves . J. Algebra 144 : 273 – 343 .
   Web of Science ®Google Scholar
• Happel , D. , Ringel , C. M. ( 1982 ). Tilted algebras . Trans. Amer. Math. Soc. 274 : 399 – 443 .
   Web of Science ®Google Scholar
• Hübner , T. ( 1998 ). Hereditary module categories arising as categories perpendicular to exceptional vector bundles . Algebras and modules, II (Geiranger, 1996) . CMS Conf. Proc. 24 . Providence, RI : Amer. Math. Soc. , pp. 327 – 336 .
   Google Scholar
• Lenzing , H. ( 1997 ). Hereditary noetherian categories with a tilting complex . Proc. AMS 125 ( 7 ): 1893 – 1901 .
   Web of Science ®Google Scholar
• Lenzing , H. , Meltzer , H. ( 1993 ). Sheaves on a weighted projective line of genus one and representations of a tubular algebra. Representation theory of algebras . Sixth International Conference, Ottawa 1992. CMS Conf. Proc. 14 , pp. 313 – 337 .
   Google Scholar
• Lenzing , H. , Skowronski , A. ( 1996 ). Quasi-tilted algebras of canonical type . Colloq. Math. 71 : 161 – 181 .
   Google Scholar
• Meltzer , H. ( 1995 ). Exceptional sequences for canonical algebras . Arch. Math. 64 : 304 – 312 .
   Web of Science ®Google Scholar
• Meltzer , H. ( 1997 ). Tubular mutations . Colloq. Math. 74 : 267 – 274 .
   Google Scholar
• Meltzer , H. Exceptional modules for tubular canonical algebras . To appear in Algebras and Representation Theory .
   Google Scholar
• Ringel , C. M. ( 1984 ). Tame Algebras and Integral Quadratic Forms . Springer Lecture Notes in Mathematics 1099 .
   Google Scholar
• Ringel , C. M. ( 1996 ). Exceptional objects in hereditary categories . An. Stiint. Univ. “Ovidius” Constanta, Ser. Mat. 4 ( 2 ): 150 – 158 .
   Google Scholar
• Ringel , C. M. ( 1998 ). Exceptional modules are tree modules . Linear Algebra and Its Applications 275–276 : 471 – 493 .
   Web of Science ®Google Scholar
• Rudakov , A. N. (ed.) ( 1990 ). Helices and vector bundles: Seminaire Rudakov . London Math. Soc . Lecture Notes, Vol. 148 .
   Google Scholar
• Schofield , A. ( 1991 ). Semi-invariants of quivers . J. Lond. Math. Soc., II. Ser. 43 ( 3 ): 385 – 395 .
   Google Scholar