Generalized cluster-tilted algebras

Details Generalized cluster-tilted algebras Generalized cluster-tilted algebras

2009-02-18

arxiv.org/abs/0902.3047v1

Mathematics

Representation Theory

10 pages

Scientific paper

Let $H$ be a finite dimensional hereditary algebra over an algebraically closed field $k$ and $\mathscr{C}_{F^m}$ be the generalized cluster category of $H$ with $m\geq 1$. We investigate the properties of generalized cluster tilting objects in $\mathscr{C}_{F^m}$ and the structure of generalized cluster-tilted algebras. Moreover, we generalized Theorem 4.2 in [A. Buan, R. Marsh, I. Reiten. 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.

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