%0 Journal Article
%T Fundamental domains of cluster categories inside module categories
%A Juan ¨¢ngel Cappa
%A Maria In¨¦s Platzeck
%A Idun Reiten
%J Mathematics
%D 2011
%I arXiv
%X Let $H$ be a finite dimensional hereditary algebra over an algebraically closed field, and let $\mathcal{C}_{H}$ be the corresponding cluster category. We give a description of the (standard) fundamental domain of $\mathcal{C}_{H} $ in the bounded derived category $\mathcal{D}^{b}(H)$, and of the cluster-tilting objects, in terms of the category $\mod\Gamma $\ of finitely generated modules over a suitable tilted algebra $% \Gamma .$ Furthermore, we apply this description to obtain (the quiver of) an arbitrary cluster-tilted algebra.
%U http://arxiv.org/abs/1112.5896v1