Cluster-tilted and quasi-tilted algebras

Ibrahim Assem; Ralf Schiffler; Khrystyna Serhiyenko

doi:10.1016/j.jpaa.2016.12.008

Cluster-tilted and quasi-tilted algebras

Ibrahim Assem, Ralf Schiffler, Khrystyna Serhiyenko

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this paper, we prove that relation-extensions of quasi-tilted algebras are 2-Calabi–Yau tilted. With the objective of describing the module category of a cluster-tilted algebra of euclidean type, we define the notion of reflection so that any two local slices can be reached one from the other by a sequence of reflections and coreflections. We then give an algorithmic procedure for constructing the tubes of a cluster-tilted algebra of euclidean type. Our main result characterizes quasi-tilted algebras whose relation-extensions are cluster-tilted of euclidean type.

Original language	English
Pages (from-to)	2266-2288
Number of pages	23
Journal	Journal of Pure and Applied Algebra
Volume	221
Issue number	9
DOIs	https://doi.org/10.1016/j.jpaa.2016.12.008
State	Published - Sep 1 2017

Bibliographical note

Funding Information:
The first author gratefully acknowledges partial support from the NSERC of Canada. The second author was supported by the NSF CAREER grant DMS-1254567 and by the University of Connecticut. The third author was supported by the NSF Postdoctoral fellowship MSPRF-1502881.

Publisher Copyright:
© 2016 Elsevier B.V.

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2016.12.008

Cite this

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Cluster-tilted and quasi-tilted algebras

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