The Ingalls-Thomas Bijections
Representation Theory
2015-12-01 v1
Abstract
Given a finite acyclic quiver Q with path algebra kQ, Ingalls and Thomas have exhibited a bijection between the set of Morita equivalence classes of support-tilting modules and the set of thick subcategories of mod kQ and they have collected a large number of further bijections with these sets. We add some additional bijections and show that all these bijections hold for arbitrary hereditary artin algebras. The proofs presented here seem to be of interest also in the special case of the path algebra of a quiver.
Keywords
Cite
@article{arxiv.1511.09391,
title = {The Ingalls-Thomas Bijections},
author = {Mustafa A. A. Obaid and S. Khalid Nauman and Wafaa M. Fakieh and Claus Michael Ringel},
journal= {arXiv preprint arXiv:1511.09391},
year = {2015}
}
Comments
This is a modified version of an appendix which was written for the paper "The numbers of support-tilting modules for a Dynkin algebra" (see arXiv:1403.5827v1)