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Tilting in Abelian Categories and Quasitilted Algebras
 
Dieter Happel Technical University of Chemnitz
Idun Reiten University of Trondheim
Sverre O. Smalo University of Trondheim
Tilting in Abelian Categories and Quasitilted Algebras
eBook ISBN:  978-1-4704-0160-3
Product Code:  MEMO/120/575.E
List Price: $44.00
MAA Member Price: $39.60
AMS Member Price: $26.40
Tilting in Abelian Categories and Quasitilted Algebras
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Tilting in Abelian Categories and Quasitilted Algebras
Dieter Happel Technical University of Chemnitz
Idun Reiten University of Trondheim
Sverre O. Smalo University of Trondheim
eBook ISBN:  978-1-4704-0160-3
Product Code:  MEMO/120/575.E
List Price: $44.00
MAA Member Price: $39.60
AMS Member Price: $26.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1201996; 88 pp
    MSC: Primary 16; 18

    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.

    Readership

    Graduate students and research mathematicians interested in associative rings and algebras.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • I. Tilting in abelian categories
    • II. Almost hereditary algebras
    • III. One point extensions of quasitilted algebras
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1201996; 88 pp
MSC: Primary 16; 18

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.

Readership

Graduate students and research mathematicians interested in associative rings and algebras.

  • Chapters
  • Introduction
  • I. Tilting in abelian categories
  • II. Almost hereditary algebras
  • III. One point extensions of quasitilted algebras
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.