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Author

Dieter Happel

Bio: Dieter Happel is an academic researcher. The author has contributed to research in topics: Quadratic algebra & Algebra representation. The author has an hindex of 1, co-authored 1 publications receiving 1717 citations.

Papers
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MonographDOI
11 Feb 1988
TL;DR: The use of triangulated categories in the study of representations of finite-dimensional algebras has been studied extensively in the literature as discussed by the authors, and triangulation is a useful tool in studying tilting processes.
Abstract: This book is an introduction to the use of triangulated categories in the study of representations of finite-dimensional algebras. In recent years representation theory has been an area of intense research and the author shows that derived categories of finite-dimensional algebras are a useful tool in studying tilting processes. Results on the structure of derived categories of hereditary algebras are used to investigate Dynkin algebras and interated tilted algebras. The author shows how triangulated categories arise naturally in the study of Frobenius categories. The study of trivial extension algebras and repetitive algebras is then developed using the triangulated structure on the stable category of the algebra's module category. With a comprehensive reference section, algebraists and research students in this field will find this an indispensable account of the theory of finite-dimensional algebras.

1,815 citations


Cited by
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Journal ArticleDOI
TL;DR: In this paper, the notion of mutation of n-cluster tilting subcategories in a triangulated category with Auslander-Reiten-Serre duality was introduced.
Abstract: We introduce the notion of mutation of n-cluster tilting subcategories in a triangulated category with Auslander–Reiten–Serre duality. Using this idea, we are able to obtain the complete classifications of rigid Cohen–Macaulay modules over certain Veronese subrings.

575 citations

Book
22 Jul 2007
TL;DR: Torsion pairs in abelian and triangulated categories Torsion pair in pretriangulated classes Compactly generated torsions in triangulation categories Hereditary torsion paired in triagonality categories TORSion pairs and closed model structures (Co)torsions and generalized Tate-Vogel cohomology Nakayama categories and Cohen-Macaulay cohology Bibliography Index as mentioned in this paper.
Abstract: Introduction Torsion pairs in abelian and triangulated categories Torsion pairs in pretriangulated categories Compactly generated torsion pairs in triangulated categories Hereditary torsion pairs in triangulated categories Torsion pairs in stable categories Triangulated torsion(-free) classes in stable categories Gorenstein categories and (co)torsion pairs Torsion pairs and closed model structures (Co)torsion pairs and generalized Tate-Vogel cohomology Nakayama categories and Cohen-Macaulay cohomology Bibliography Index.

447 citations

Posted Content
TL;DR: Differential graded categories enhance our understanding of triangulated categories appearing in algebra and geometry as discussed by the authors, and they have been extensively studied in recent work by Drinfeld, Dugger-Shipley,..., Toen and Toen-Vaquie.
Abstract: Differential graded categories enhance our understanding of triangulated categories appearing in algebra and geometry. In this survey, we review their foundations and report on recent work by Drinfeld, Dugger-Shipley, ..., Toen and Toen-Vaquie.

442 citations

Journal ArticleDOI
TL;DR: In this paper, the authors consider the formation of the subcategories right (left) perpendicular to a subcategory of objects in an abelian category, and show the applicability of this concept in finite dimensional algebras and their representations.

431 citations