Covering functors without groups

Details Covering functors without groups Covering functors without groups

2008-03-31

arxiv.org/abs/0803.4442v3

J. Algebra 321 (2009), 3816-3826

Mathematics

Representation Theory

Some improvements have been made; in particular, the proof of Theorem 2 has been restructured and clarified

Scientific paper

10.1016/j.jalgebra.2009.02.023

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.

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