Skip to Main content Skip to Navigation
Theses

Revêtements galoisiens et groupe fondamental d'algèbres de dimension finie

Abstract : This thesis is devoted to the study of the Galois coverings of finite dimensional algebras. In particular, it investigates the existence of a universal cover and a fundamental group for finite dimensional connected and basic algebras over an algebraically closed field. For this purpose, we start from an already existing notion: the fundamental group associated with any presentation of such an algebra A by its ordinary quiver Q and admissible relations. We first compare the different presentations of A. The automorphisms of the path algebra kQ allow one to link two arbitrary presentations of A. Among these automorphisms, we distinguish the dilatations and the transvections: they generate the group of automorphisms of kQ, moreover, the fundemantal groups of two presentations of A linked by a transvection or a dilatation are related by a quotient relation. These properties allow us to exhibit a fundamental group for A when the ground field has characteristic zero and when Q has no double bypass. These considerations can be translated in terms of Galois coverings since any presentation gives rise to a Galois covering with group the fundamental group of the presentation. Hence, under the above hypotheses granting a fundamental group, A admits a universal cover. This last result is extended to the case where A is monomial, Q has no oriented cycles and no multiple arrows (but may have double bypasses) and where the ground field may have any characteristic.
Document type :
Theses
Complete list of metadatas

Cited literature [39 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00011753
Contributor : Patrick Le Meur <>
Submitted on : Tuesday, December 5, 2006 - 2:06:27 PM
Last modification on : Monday, November 18, 2019 - 1:32:07 PM
Long-term archiving on: : Monday, September 17, 2012 - 12:21:09 PM

Files

Identifiers

  • HAL Id : tel-00011753, version 1

Citation

Patrick Le Meur. Revêtements galoisiens et groupe fondamental d'algèbres de dimension finie. Mathématiques [math]. Université Montpellier II - Sciences et Techniques du Languedoc, 2006. Français. ⟨tel-00011753⟩

Share

Metrics

Record views

377

Files downloads

945