English

Continuous cluster categories II: continuous cluster-tilted categories

Representation Theory 2019-09-13 v1

Abstract

We show that the quotient of the continuous cluster category Cπ\mathcal C_\pi modulo the additive subcategory generated by any cluster is an abelian category and we show that it is isomorphic to the category of infinite length modules over the endomorphism ring of the cluster. These theorems extend the theorems of Caldero-Chapoton-Schiffler and Buan-Marsh-Reiten for cluster categories to the continuous cluster category of type AA. These results will be generalized in a series of forthcoming joint papers of the two authors with Job Rock.

Keywords

Cite

@article{arxiv.1909.05340,
  title  = {Continuous cluster categories II: continuous cluster-tilted categories},
  author = {Kiyoshi Igusa and Gordana Todorov},
  journal= {arXiv preprint arXiv:1909.05340},
  year   = {2019}
}

Comments

This paper needs to be updated with more references

R2 v1 2026-06-23T11:12:50.471Z