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Mathematics > Representation Theory

arXiv:1801.04989 (math)
[Submitted on 15 Jan 2018 (v1), last revised 18 Oct 2018 (this version, v2)]

Title:$m$-cluster tilted algebras of euclidean type

Authors:Elsa Fernández, Ana Garcia Elsener, Sonia Trepode
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Abstract:We consider $m$-cluster tilted algebras arising from quivers of Euclidean type and we give necessary and sufficient conditions for those algebras to be representation finite. For the case $\widetilde{A}$, using the geometric realization, we get a description of representation finite type in terms of $(m+2)$-angulations. We establish which $m$-cluster tilted algebras arise at the same time from quivers of type $A$ and $\widetilde{A}$. Finally, we characterize representation infinite $m$-cluster tilted algebras arising from a quiver of type $\widetilde{A}$ as $m$-relations extensions of some iterated tilted algebra of type $\widetilde{A}$.
Comments: v1: 14 pages, 10 figures, presented at the ICRA 2016 - Syracuse - v2: 17 pages, to appear in this http URL
Subjects: Representation Theory (math.RT); Rings and Algebras (math.RA)
MSC classes: 16G20 - 16G60
Cite as: arXiv:1801.04989 [math.RT]
  (or arXiv:1801.04989v2 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.1801.04989

Submission history

From: Ana Garcia Elsener [view email]
[v1] Mon, 15 Jan 2018 20:28:29 UTC (71 KB)
[v2] Thu, 18 Oct 2018 20:53:54 UTC (57 KB)
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