Rigid objects in higher cluster categories

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dc.creatorWrålsen, Anette
dc.date2007-12-18
dc.date2009-02-10
dc.date.accessioned2026-07-07T12:39:03Z
dc.date.available2026-07-07T12:39:03Z
dc.descriptionWe study maximal $m$-rigid objects in the $m$-cluster category $\mathcal C_H^m$ associated with a finite dimensional hereditary algebra $H$ with $n$ nonisomorphic simple modules. We show that all maximal $m$-rigid objects in these categories have exactly $n$ nonisomorphic indecomposable summands, and that any almost complete $m$-rigid object in $\mathcal C_H^m$ has exactly $m+1$ nonisomorphic complements. We also show that the maximal $m$-rigid objects and the $m$-cluster tilting objects in these categories coincide, and that the class of finite dimensional algebras associated with maximal $m$-rigid objects is closed under certain factor algebras.
dc.description2nd version 17 pages. More details have been added and some proofs have been improved. Some references have also been added
dc.identifierhttps://arxiv.org/abs/0712.2970
dc.identifierhttp://arxiv.org/abs/0712.2970
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/218976
dc.subjectRepresentation Theory
dc.subject16G20; 16G70
dc.titleRigid objects in higher cluster categories
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