Covering functors without groups
Abstract
Coverings in the representation theory of algebras were introduced for the Auslander-Reiten quiver of a representation finite algebra by Riedtmann and later for finite dimensional algebras by Bongartz and Gabriel, R. Martinez-Villa and de la Pe\~na. The best understood class covering functors is that of Galois covering functors F: A -> B determined by the action of a group of automorphisms of A. In this work we introduce the balanced covering functors which include the Galois class and for which classical Galois covering-type results still hold. For instance, if F:A -> B is a balanced covering functor, where A and B are linear categories over an algebraically closed field, and B is tame, then A is tame.
Cite
@article{arxiv.0803.4442,
title = {Covering functors without groups},
author = {Jose Antonio de la Peña and Maria Julia Redondo},
journal= {arXiv preprint arXiv:0803.4442},
year = {2010}
}
Comments
Some improvements have been made; in particular, the proof of Theorem 2 has been restructured and clarified