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 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 A. Finally, we characterize representation infinite m-cluster tilted algebras arising from a quiver of type A˜, as m-relations extensions of some iterated tilted algebra of type A˜.

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