From iterated tilted algebras to cluster-tilted 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.
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 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.
متن کاملAuslander Generators of Iterated Tilted Algebras
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...
متن کاملCluster-tilted algebras and their intermediate coverings
We construct the intermediate coverings of cluster-tilted algebras by defining the generalized cluster categories. These generalized cluster categories are Calabi-Yau triangulated categories with fraction CY-dimension and have also cluster tilting objects (subcategories). Furthermore we study the representations of these intermediate coverings of cluster-tilted algebras.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2010
ISSN: 0001-8708
DOI: 10.1016/j.aim.2009.10.004