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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