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Tilting in Abelian Categories and Quasitilted Algebras

Dieter HappelIdun ReitenSverre O. Smalø

出版	American Mathematical Soc., 1996
主題	Mathematics / GeneralMathematics / Algebra / GeneralMathematics / Set Theory
ISBN	08218044489780821804445
URL	http://books.google.com.hk/books?id=9HPTCQAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

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.