Projective Dimension of Modules over Cluster-Tilted Algebras
نویسندگان
چکیده
منابع مشابه
On 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...
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15 صفحه اولCluster-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 کاملFrom 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.
متن کاملCluster-tilted algebras and slices
We give a criterion allowing to verify whether or not two tilted algebras have the same relation-extension (thus correspond to the same cluster-tilted algebra). This criterion is in terms of a combinatorial configuration in the Auslander-Reiten quiver of the cluster-tilted algebra, which we call local slice.
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2014
ISSN: 1386-923X,1572-9079
DOI: 10.1007/s10468-014-9472-0