#### Vol. 4, No. 5, 2010

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Connected gradings and the fundamental group

### Claude Cibils, María Julia Redondo and Andrea Solotar

Vol. 4 (2010), No. 5, 625–648
##### Abstract

The main purpose of this paper is to provide explicit computations of the fundamental groups 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.

##### Keywords
grading, Galois covering, fundamental group
Primary: 16W50
Secondary: 16S50
##### Milestones
Received: 24 November 2009
Accepted: 1 April 2010
Published: 10 July 2010
##### Authors
 Claude Cibils Institut de mathématiques et de modélisation de Montpellier I3M UMR 5149 Université Montpellier 2 F-34095 Montpellier cedex 5 France http://www.math.univ-montp2.fr/~cibils/ María Julia Redondo Departamento de Matemática Universidad Nacional del Sur Avenida Leandro N. Alem 1253 B8000CPB Bahía Blanca Argentina http://inmabb.criba.edu.ar/gente/mredondo/ Andrea Solotar Departamento de Matemática Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires Ciudad Universitaria, Pabellón 1 C1428EGA Buenos Aires Argentina http://mate.dm.uba.ar/~asolotar