$m$-cluster categories and $m$-replicated algebras

Assem, I.; Brüstle, T.; Schiffler, R.; Todorov, G.

$m$-cluster categories and $m$-replicated algebras

Authors

Description

Let A be a hereditary algebra over an algebraically closed field. We prove that an exact fundamental domain for the m-cluster category of A is the m-left part of the m-replicated algebra $A^{(m)}$ of A. Moreover, we obtain a one-to-one correspondence between the tilting objects in the m-cluster category (that is, the m-clusters) and those tilting $A^{(m)}$-modules for which all non projective-injective direct summands lie in the m-left part of $A^{(m)}$.
28 pages, 2 figures