Tilting in abelian categories and quasitilted algebras
About this Title
Dieter Happel, Idun Reiten and SmaløSverre O.
Publication: Memoirs of the American Mathematical Society
Publication Year 1996: Volume 120, Number 575
ISBNs: 978-0-8218-0444-5 (print); 978-1-4704-0160-3 (online)
MathSciNet review: 1327209
MSC (1991): Primary 16D90; Secondary 16G10, 18E10, 18E40
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.
Graduate students and research mathematicians interested in associative rings and algebras.
Table of Contents
- I. Tilting in abelian categories
- II. Almost hereditary algebras
- III. One point extensions of quasitilted algebras