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arXiv · 0912.0298

Cluster-tilted algebras without clusters

Ibrahim Assem·Thomas Bruestle·Ralf Schiffler
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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.

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Ibrahim Assem, Thomas Bruestle, Ralf Schiffler. 2009-12-01. Cluster-tilted algebras without clusters. https://arxiv.org/abs/0912.0298

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