Coxeter functors without diagrams
About:
This article is published in Transactions of the American Mathematical Society.The article was published on 1979-06-01 and is currently open access. It has received 307 citations till now. The article focuses on the topics: Coxeter group & Functor.read more
Citations
More filters
Journal ArticleDOI
Tilting theory and cluster combinatorics
TL;DR: In this article, a new category C, called the cluster category, is introduced, which is obtained as a quotient of the bounded derived category D of the module category of a finite-dimensional hereditary algebra H over a field.
Posted Content
Tilting theory and cluster combinatorics
TL;DR: In this paper, a new category C, called the cluster category, which is obtained as a quotient of the bounded derived category D of the module category of a finite-dimensional hereditary algebra H over a field, is introduced.
Journal ArticleDOI
Mutation in triangulated categories and rigid Cohen–Macaulay modules
Osamu Iyama,Yuji Yoshino +1 more
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.
Journal ArticleDOI
Cluster-tilted algebras
TL;DR: Cluster-tilted algebras as discussed by the authors are the endomorphism algesms of tilting objects in a cluster category, and their representation theory is very close to the representation theory of hereditary algesbras.
References
More filters
Book
Graduate Texts in Mathematics
Rajendra Bhatia,Glen Bredon,Wolfgang Walter,Joseph J. Rotman,M. Ram Murty,Jane Gilman,Peter Walters,Martin Golubitsky,Ioannis Karatzas,Henri Cohen,Raoul Bott,Gaisi Takeuti,Béla Bollobás,John M. Lee,Jiří Matoušek,Saunders Mac Lane,John L. Kelley,B. A. Dubrovin,Tom M. Apostol,John Stillwell,William Arveson +20 more
Book
Rings and Categories of Modules
Frank W. Anderson,Kent R. Fuller +1 more
TL;DR: In this paper, the authors provide a self-contained account of much of the theory of rings and modules, focusing on the relationship between the one-sided ideal structure a ring may possess and the behavior of its categories of modules.
Journal ArticleDOI
Representation Theory of Artin Algebras I
TL;DR: The first of a series of papers dealing with the representation theory of artin algebras is presented in this paper, where the main purpose is to develop terminology and background material which will be used in the rest of the papers in the series.
Journal ArticleDOI
Coxeter functors and gabriel's theorem
TL;DR: In this article, the Coxeter-Weyl group and Dynkin diagrams are connected with the theory of infinite-dimensional Lie algebras. But they do not touch on the connections between these questions and group representations.
Journal ArticleDOI
Representation theory of artin algebras iii almost split sequences
Maurice Auslander,Idun Reiten +1 more
TL;DR: In this paper, the representation theory of artin algebras iii almost split sequences is studied and the authors propose a representation theory for almost-split sequences in algebraic graphs.