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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Tilting objects in abelian categories and quasitilted rings


Authors: Riccardo Colpi and Kent R. Fuller
Journal: Trans. Amer. Math. Soc. 359 (2007), 741-765
MSC (2000): Primary 16E10, 16G99, 16S50, 18E40, 18E25, 18G20; Secondary 16B50, 16D90
Published electronically: August 24, 2006
MathSciNet review: 2255195
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Abstract: D. Happel, I. Reiten and S. Smalø initiated an investigation of quasitilted artin $ K$-algebras that are the endomorphism rings of tilting objects in hereditary abelian categories whose Hom and Ext groups are all finitely generated over a commutative artinian ring $ K$. Here, employing a notion of $ \ast $-objects, tilting objects in arbitrary abelian categories are defined and are shown to yield a version of the classical tilting theorem between the category and the category of modules over their endomorphism rings. This leads to a module theoretic notion of quasitilted rings and their characterization as endomorphism rings of tilting objects in hereditary cocomplete abelian categories.


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Additional Information

Riccardo Colpi
Affiliation: Department of Pure and Applied Mathematics, University of Padova, via Belzoni 7, I 35100 Padova, Italy
Email: colpi@math.unipd.it

Kent R. Fuller
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242-1419
Email: kfuller@math.uiowa.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03909-2
PII: S 0002-9947(06)03909-2
Received by editor(s): September 21, 2004
Received by editor(s) in revised form: December 3, 2004
Published electronically: August 24, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.