A brick version of a theorem of Auslander

Francesco Sentieri

A brick version of a theorem of Auslander

Representation Theory 2020-11-19 v1

Authors: Francesco Sentieri

Abstract

We prove that a finite dimensional algebra $\Lambda$ is $\tau-$ tilting finite if and only if all the bricks over $\Lambda$ are finitely generated. This is obtained as a consequence of the existence of proper locally maximal torsion classes for $\tau-$ tilting infinite algebras.

Keywords

finite dimensional algebra tau-tilting finite bricks torsion classes auslander theorem

Cite

@article{arxiv.2011.09253,
  title  = {A brick version of a theorem of Auslander},
  author = {Francesco Sentieri},
  journal= {arXiv preprint arXiv:2011.09253},
  year   = {2020}
}

Comments

17 pages, 1 figure

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