Tilting in Abelian Categories and Quasitilted Algebras

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Tilting in Abelian Categories and Quasitilted Algebras is written by Dieter Happel and published by American Mathematical Soc.. It's available with International Standard Book Number or ISBN identification 0821804448 (ISBN 10) and 9780821804445 (ISBN 13).

We generalize tilting 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. Our construction is motivated by the connection between tilting and derived categories. We develop a general theory for such tilting, and are led to a generalization of tilting algebras which we call quasitilted algebras. This class also contains the canonical algebras, and we 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. We also give other characterizations of quasitilted algebras, and give methods for constructing such algebras.