Covering functors without groups

TL;DR

This paper introduces balanced covering functors in the representation theory of algebras, extending Galois coverings to a broader class where classical results like tameness preservation still hold.

Contribution

It defines balanced covering functors that generalize Galois coverings and proves that tameness is preserved under these functors.

Findings

Balanced coverings include Galois coverings.

Tameness of B implies tameness of A under balanced coverings.

Classical Galois covering results extend to this broader class.

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.