Constructing tilted algebras from cluster-tilted algebras

Abstract

Any cluster-tilted algebra is the relation extension of a tilted algebra. We present a method to, given the distribution of a cluster-tilting object in the Auslander-Reiten quiver of the cluster category, construct all tilted algebras whose relation extension is the endomorphism ring of this cluster-tilting object.

Section 3 has been removed and now is an independent article (arXiv:0912.2911v1). Section 1 and 2.2 have been modified to cope with the removal of section 3. Proof of theorem 3.5 (previously 4.5) has been improved. More details have been added to section 6 (previously 7) to clarify how section 3 (previously 4) generalizes to the infinite case

References in corpus (5)

• Deformed Calabi-Yau Completions
• From tilted to cluster-tilted algebras of Dynkin type
• The mutation class of $D_n$ quivers
• A Criterion for global dimension two for strongly simply connected schurian algebras
• Finding a cluster-tilting object for a representation finite cluster-tilted algebra

Cited by in corpus (1)

• Projective Dimensions and Extensions of Modules from Titled to Cluster-Tilted Algebras