$m$-cluster tilted algebras of euclidean type

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

v1: 14 pages, 10 figures, presented at the ICRA 2016 - Syracuse - v2: 17 pages, to appear in J.Algebra