English

Torsion classes, wide subcategories and localisations

Representation Theory 2017-06-19 v2 Rings and Algebras

Abstract

For a finite dimensional algebra AA, we establish correspondences between torsion classes and wide subcategories in mod(A)mod(A). In case AA is representation finite, we obtain an explicit bijection between these two classes of subcategories. Moreover, we translate our results to the language of ring epimorphisms and universal localisations. It turns out that universal localisations over representation finite algebras are classified by torsion classes and support τ\tau-tilting modules.

Keywords

Cite

@article{arxiv.1503.04639,
  title  = {Torsion classes, wide subcategories and localisations},
  author = {Frederik Marks and Jan Stovicek},
  journal= {arXiv preprint arXiv:1503.04639},
  year   = {2017}
}

Comments

13 pages; version 2: new Example 4.7 based on arXiv:1610.05860, small changes in presentation, updated references

R2 v1 2026-06-22T08:54:01.292Z