#### 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.