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Tilting in Abelian Categories and Quasitilted Algebras (Memoirs of the American Mathematical Society)
Rok: 1996
ISBN: 9780821804445
OKCZID: 110416172
Citace (dle ČSN ISO 690):
HAPPEL, Dieter. Tilting in Abelian categories and quasitilted algebras. Providence, R.I.: American Mathematical Society, c1996. vi, 88 s. Memoirs of the American Mathematical Society, 575.
Anotace
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.