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arxiv: 1801.04989 · v2 · pith:2V77ZYEPnew · submitted 2018-01-15 · 🧮 math.RT · math.RA

m-cluster tilted algebras of euclidean type

classification 🧮 math.RT math.RA
keywords typealgebrastiltedclusterwidetilderepresentationarisingeuclidean
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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 $\widetilde{A}$.

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