Two classes of almost Galois coverings for algebras

Piotr Dowbor, and Adam Hajduk. "Two classes of almost Galois coverings for algebras." Colloquium Mathematicae 127.2 (2012): 253-298. <http://eudml.org/doc/283675>.

@article{PiotrDowbor2012,
abstract = {We prove that for any representation-finite algebra A (in fact, finite locally bounded k-category), the universal covering F: Ã → A is either a Galois covering or an almost Galois covering of integral type, and F admits a degeneration to the standard Galois covering F̅: Ã→ Ã/G, where $G = Π(Γ_A)$ is the fundamental group of $Γ_A$. It is shown that the class of almost Galois coverings F: R → R’ of integral type, containing the series of examples from our earlier paper [Bol. Soc. Mat. Mexicana 17 (2011)], behaves much more regularly than usual with respect to the standard properties of the pair $(F_λ, F_•)$ of adjoint functors associated to F.},
author = {Piotr Dowbor, Adam Hajduk},
journal = {Colloquium Mathematicae},
keywords = {finite dimensional algebras; representation-finite algebras; cover categories; representation types; indecomposable modules; covering functors; degenerations; locally bounded categories; almost Galois coverings; quivers; fundamental groups},
language = {eng},
number = {2},
pages = {253-298},
title = {Two classes of almost Galois coverings for algebras},
url = {http://eudml.org/doc/283675},
volume = {127},
year = {2012},
}

TY - JOUR
AU - Piotr Dowbor
AU - Adam Hajduk
TI - Two classes of almost Galois coverings for algebras
JO - Colloquium Mathematicae
PY - 2012
VL - 127
IS - 2
SP - 253
EP - 298
AB - We prove that for any representation-finite algebra A (in fact, finite locally bounded k-category), the universal covering F: Ã → A is either a Galois covering or an almost Galois covering of integral type, and F admits a degeneration to the standard Galois covering F̅: Ã→ Ã/G, where $G = Π(Γ_A)$ is the fundamental group of $Γ_A$. It is shown that the class of almost Galois coverings F: R → R’ of integral type, containing the series of examples from our earlier paper [Bol. Soc. Mat. Mexicana 17 (2011)], behaves much more regularly than usual with respect to the standard properties of the pair $(F_λ, F_•)$ of adjoint functors associated to F.
LA - eng
KW - finite dimensional algebras; representation-finite algebras; cover categories; representation types; indecomposable modules; covering functors; degenerations; locally bounded categories; almost Galois coverings; quivers; fundamental groups
UR - http://eudml.org/doc/283675
ER -