Connected gradings and fundamental group.

Claude Cibils (1) , Maria Julia Redondo (2) , Andrea Solotar (3)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 DEPARTAMENTO DE MATEMATICA UNS - Departamento de Matematica
3 Departamento de Matemática [Buenos Aires]

The main purpose of this paper is to provide explicit computations of the fundamental group of several algebras. For this purpose, given a $k$-algebra $A$, we consider the category of all connected gradings of $A$ by a group $G$ and we study the relation between gradings and Galois coverings. This theoretical tool gives information about the fundamental group of $A$, which allows its computation using complete lists of gradings.

Mots clés: grading; Galois covering; fundamental group

Domaines: Anneaux et algèbres [math.RA]; K-théorie et homologie [math.KT]; Théorie des représentations [math.RT]; Algèbres quantiques [math.QA]

Claude Cibils, Maria Julia Redondo, Andrea Solotar. Connected gradings and fundamental group.. Algebra & Number Theory, 2010, 4 (5), pp.625--648. ⟨10.2140/ant.2010.4.625⟩. ⟨hal-00396120v3⟩