Galois coverings of weakly shod algebras

Patrick Le Meur (1)

1 CMLA - Centre de Mathématiques et de Leurs Applications

We investigate the Galois coverings of weakly shod algebras. For a weakly shod algebra not quasi-tilted of canonical type, we establish a correspondence between its Galois coverings and the Galois coverings of its connecting component. As a consequence, we show that a weakly shod algebra is simply connected if and only if its first Hochschild cohomology group vanishes.

Mots clés: representations; finite dimensional algebras; tilted; quasi-tilted; weakly shod; laura; Galois covering; fundamental group; simply connected

Domaines: Théorie des représentations [math.RT]

Patrick Le Meur. Galois coverings of weakly shod algebras. Communications in Algebra, 2010, 38 (4), pp.1291--1318. ⟨10.1080/00927870902897939⟩. ⟨hal-00325669v2⟩