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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hereditary noetherian categories
with a tilting complex


Author: Helmut Lenzing
Journal: Proc. Amer. Math. Soc. 125 (1997), 1893-1901
MSC (1991): Primary 14G14, 16G20; Secondary 18F20, 18E30
MathSciNet review: 1423314
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Abstract: We are characterizing the categories of coherent sheaves on a weighted projective line as the small hereditary noetherian categories without projectives and admitting a tilting complex. The paper is related to recent work with de la Peña (Math. Z., to appear) characterizing finite dimensional algebras with a sincere separating tubular family, and further gives a partial answer to a question of Happel, Reiten, Smalø (Mem. Amer. Math. Soc. 120 (1996), no. 575) regarding the characterization of hereditary categories with a tilting object.


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Additional Information

Helmut Lenzing
Affiliation: Universität-GH Paderborn, Fachbereich Mathematik-Informatik, D-33095 Pader- born, Germany
Email: helmut@uni-paderborn.de

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04122-1
PII: S 0002-9939(97)04122-1
Keywords: Weighted projective line, coherent sheaf, almost-split sequence, Auslander-Reiten theory, finite dimensional algebra, quiver, derived category, exceptional object, tilting complex.
Received by editor(s): February 9, 1995
Dedicated: In memory of Maurice Auslander
Communicated by: Eric M. Friedlander
Article copyright: © Copyright 1997 American Mathematical Society