Tilting objects in abelian categories and quasitilted rings

Colpi, Riccardo; Fuller, Kent

doi:10.1090/S0002-9947-06-03909-2

Tilting objects in abelian categories and quasitilted rings
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by Riccardo Colpi and Kent R. Fuller PDF

Trans. Amer. Math. Soc. 359 (2007), 741-765 Request permission

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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