Connected gradings and fundamental group

Details Connected gradings and fundamental group Connected gradings and fundamental group

2009-06-17

arxiv.org/abs/0906.3069v4

Mathematics

Rings and Algebras

Final version to appear in Algebra & Number Theory. 26 pages

Scientific paper

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.

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