Fundamental domains of cluster categories inside module categories

Abstract

Let H be a finite dimensional hereditary algebra over an algebraically closed field, and let CH be the corresponding cluster category. We give a description of the (standard) fundamental domain of CH in the bounded derived category D b(H), and of the cluster-tilting objects, in terms of the category modΓ of finitely generated modules over a suitable tilted algebra Γ. Furthermore, we apply this description to obtain (the quiver of) an arbitrary cluster-tilted algebra.