Repetitive cluster-tilted algebras

Abstract

Let $H$ be a finite dimensional hereditary algebra over an algebraically closed field $k$ and $\mathscr{C}_{F^m}$ be the repetitive cluster category of $H$ with $m\geq 1$. We investigate the properties of cluster tilting objects in $\mathscr{C}_{F^m}$ and the structure of repetitive cluster-tilted algebras. Moreover, we generalized Theorem 4.2 in \cite{bmrrt} (Buan A, Marsh R, Reiten I. Cluster-tilted algebra. Trans. Amer. Math. Soc., 359(1)(2007), 323-332.) to the situation of $\mathscr{C}_{F^m}$, and prove that the tilting graph $\mathscr{K}_{\mathscr{C}_{F^m}}$ of $\mathscr{C}_{F^m}$ is connected.