Iterated tilted and tilted stably hereditary algebras
نویسندگان
چکیده
منابع مشابه
From Iterated Tilted Algebras to Cluster-tilted Algebras
In this paper the relationship between iterated tilted algebras and cluster-tilted algebras and relation-extensions is studied. In the Dynkin case, it is shown that the relationship is very strong and combinatorial.
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Let Λ be an iterated tilted algebra. We will construct an Auslander generator M in order to show that the representation dimension of Λ is three in case Λ is representation infinite. Recently there has been a lot of attention to compute the representation dimension of a finite dimensional algebra Λ, a notion introduced by Auslander in [A] in an attempt to measure the complexity of the represent...
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We prove that in a 2-Calabi-Yau triangulated category, each cluster tilting subcategory is Gorenstein with all its finitely generated projectives of injective dimension at most one. We show that the stable category of its Cohen-Macaulay modules is 3-CalabiYau. We deduce in particular that cluster-tilted algebras are Gorenstein of dimension at most one, and hereditary if they are of finite globa...
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 کاملTilted String Algebras
Tilted algebras, that is endomorphism algebras of tilting modules over a hereditary algebra, have been one of the main objects of study in representation theory of algebras since their introduction by Happel and Ringel [10]. As a generalization, Happel, Reiten and Smalø studied endomorphism algebras of tilting objects of a hereditary abelian category which they call quasi-tilted algebras [9]. T...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 2003
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm98-1-4