Trivial extensions, iterated tilted algebras and 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 کاملJa n 20 06 Cluster - tilted algebras as trivial extensions
Given a finite dimensional algebra C (over an algebraically closed field) of global dimension at most two, we define its relation-extension algebra to be the trivial extension C ⋉ Ext 2 C (DC, C) of C by the CC -bimodule Ext 2 C (DC, C). We give a construction for the quiver of the relation-extension algebra in case the quiver of C has no oriented cycles. Our main result says that an algebrã C ...
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 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: The São Paulo Journal of Mathematical Sciences
سال: 2010
ISSN: 2316-9028,1982-6907
DOI: 10.11606/issn.2316-9028.v4i3p499-527