# Tilting in Abelian Categories and Quasitilted Algebras

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*Dieter Happel; Idun Reiten; Sverre O. Smalo*

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.