A characterization of the hereditary categories derived equivalent to some category of coherent sheaves on a weighted projective line

Authors:
Dieter Happel and Idun Reiten

Journal:
Proc. Amer. Math. Soc. **130** (2002), 643-651

MSC (1991):
Primary 16B50, 16E10, 16G70, 18E10, 18E30

DOI:
https://doi.org/10.1090/S0002-9939-01-06159-7

Published electronically:
September 28, 2001

MathSciNet review:
1866014

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a connected hereditary abelian category over an algebraically closed field , with finite dimensional homomorphism and extension spaces. There are two main known types of such categories: those derived equivalent to for some finite dimensional hereditary -algebra and those derived equivalent to some category of coherent sheaves on a weighted projective line in the sense of Geigle and Lenzing (1987). The aim of this paper is to give a characterization of the second class in terms of some properties known to hold for these hereditary categories.

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Additional Information

**Dieter Happel**

Affiliation:
Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany

Email:
happel@mathematik.tu-chemnitz.de

**Idun Reiten**

Affiliation:
Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway

Email:
idunr@math.ntnu.no

DOI:
https://doi.org/10.1090/S0002-9939-01-06159-7

Received by editor(s):
January 13, 2000

Received by editor(s) in revised form:
September 12, 2000

Published electronically:
September 28, 2001

Communicated by:
Ken Goodearl

Article copyright:
© Copyright 2001
American Mathematical Society