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

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

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

表示论 2007-05-23 v1 环与代数

作者: I. Assem , T. Brüstle , R. Schiffler , G. Todorov

摘要

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 $A^{(m)}$ .

关键词

cluster algebras triangulated categories tensor category

引用

@article{arxiv.math/0608727,
  title  = {$m$-cluster categories and $m$-replicated algebras},
  author = {I. Assem and T. Brüstle and R. Schiffler and G. Todorov},
  journal= {arXiv preprint arXiv:math/0608727},
  year   = {2007}
}

备注

28 pages, 2 figures

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

摘要

关键词

引用

备注

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