Cluster-tilted algebras as trivial extensions

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dc.creatorAssem, Ibrahim
dc.creatorBrüstle, Thomas
dc.creatorSchiffler, Ralf
dc.date2006-01-23
dc.date.accessioned2026-07-07T06:59:11Z
dc.date.available2026-07-07T06:59:11Z
dc.descriptionGiven 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 $C\ltimes \Ext_C^2(DC,C)$ of $C$ by the $C$-$C$-bimodule $\Ext_C^2(DC,C)$. 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 algebra $\tilde C$ is cluster-tilted if and only if there exists a tilted algebra $C$ such that $\tilde C$ is isomorphic to the relation-extension of $C$.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/math/0601537
dc.identifierhttp://arxiv.org/abs/math/0601537
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/107654
dc.subjectRepresentation Theory
dc.subjectRings and Algebras
dc.subject16S70; 16G20
dc.titleCluster-tilted algebras as trivial extensions
dc.typetext

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