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Hereditary noetherian categories with a tilting complex
Author(s):
Helmut
Lenzing
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1893-1901.
MSC (1991):
Primary 14G14, 16G20;
Secondary 18F20, 18E30
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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:
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
Copyright of article:
Copyright
1997,
American Mathematical Society
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