Cluster-tilted algebras without clusters
Representation Theory
2009-12-03 v1 Rings and Algebras
Abstract
Cluster-tilted algebras are trivial extensions of tilted algebras. This correspondence induces a surjective map from tilted algebras to cluster-tilted algebras. If B is a cluster-tilted algebra, we use the fibre of B under this map to study the module category of B. In particular, we introduce the notion of reflections of tilted algebras and define an algorithm that constructs the transjective component of the Auslander-Reiten quiver of cluster-tilted algebras of tree type.
Cite
@article{arxiv.0912.0298,
title = {Cluster-tilted algebras without clusters},
author = {Ibrahim Assem and Thomas Bruestle and Ralf Schiffler},
journal= {arXiv preprint arXiv:0912.0298},
year = {2009}
}
Comments
37 pages