Tilting Theory and Quasitilted Algebras
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منابع مشابه
On Auslander–Reiten components for quasitilted algebras
An artin algebra A over a commutative artin ring R is called quasitilted if gl.dimA ≤ 2 and for each indecomposable finitely generated A-module M we have pdM ≤ 1 or idM ≤ 1. In [11] several characterizations of quasitilted algebras were proven. We investigate the structure and homological properties of connected components in the Auslander–Reiten quiver ΓA of a quasitilted algebra A. Let A be a...
متن کاملOn Tilting Modules over Cluster-tilted Algebras
In this paper, we show that the tilting modules over a clustertilted algebra A lift to tilting objects in the associated cluster category CH . As a first application, we describe the induced exchange relation for tilting Amodules arising from the exchange relation for tilting object in CH . As a second application, we exhibit tilting A-modules having cluster-tilted endomorphism algebras. Cluste...
متن کاملTilting Theory and Cluster Algebras
The purpose of this chapter is to give an introduction to the theory of cluster categories and cluster-tilted algebras, with some background on the theory of cluster algebras, which motivated these topics. We will also discuss some of the interplay between cluster algebras on one side and cluster categories/cluster-tilted algebras on the other, as well as feedback from the latter theory to clus...
متن کاملCluster-tilted Algebras
We introduce a new class of algebras, which we call cluster-tilted. They are by definition the endomorphism algebras of tilting objects in a cluster category. We show that their representation theory is very close to the representation theory of hereditary algebras. As an application of this, we prove a generalised version of so-called APR-tilting.
متن کاملAlmost Regular Auslander-reiten Components and Quasitilted Algebras
The problem of giving a general description of the shapes of AuslanderReiten components of an artin algebra has been settled for semiregular components (see [4, 9, 14]). Recently, S. Li has considered this problem for components in which every possible path from an injective module to a projective module is sectional. The result says that such a component is embeddable in some ZZ∆ with ∆ a quiv...
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تاریخ انتشار 1998