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

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

2006-08-29

arxiv.org/abs/math/0608727v1

Mathematics

Representation Theory

28 pages, 2 figures

Scientific paper

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 $A^{(m)}$.

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