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Tilting in Abelian Categories and Quasitilted Algebras
Dieter Happel, Technical University of Chemnitz, Germany, and Idun Reiten and Sverre O. Smalø, University of Trondheim, Dragvoll, Norway
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Memoirs of the American Mathematical Society
1996; 88 pp; softcover
Volume: 120
ISBN-10: 0-8218-0444-8
ISBN-13: 978-0-8218-0444-5
List Price: US$44 Individual Members: US$26.40
Institutional Members: US\$35.20
Order Code: MEMO/120/575

In this book, the authors generalize with respect to a tilting module of projective dimension at most one for an artin algebra to tilting with respect to a torsion pair in an abelian category. A general theory is developed for such tilting and the reader is led to a generalization for tilted algebras which the authors call "quasitilted algebras". This class also contains the canonical algebras, and the authors show that the quasitilted algebras are characterized by having global dimension at most two and each indecomposable module having projective dimension at most one or injective dimension at most one.

The authors also give other characterizations of quasitilted algebras and give methods for constructing such algebras. In particular, they investigate when one-point extensions of hereditary algebras are quasitilted.