The universal cover of an algebra without double bypass

Patrick Le Meur (1)

1 CMLA - Centre de Mathématiques et de Leurs Applications

Let A be a basic finite dimensional and connected algebra over an algebraically closed field k with zero characteristic. If the ordinary quiver of A has no double bypasses, we show that A admits a Galois covering which satisfies a universal property with respect to the Galois coverings of A. This universal property is similar to the one of the universal cover of a connected topological space.

Mots clés: quiver with relations; fundamental group; homotopy relation; covering; galois covering; covering functor; universal cover

Domaines: Théorie des représentations [math.RT]

Patrick Le Meur. The universal cover of an algebra without double bypass. Journal of Algebra, 2007, 312 (1), pp.330--353. ⟨10.1016/j.jalgebra.2006.10.035⟩. ⟨hal-00007672v4⟩