Connected gradings and the fundamental group

Cibils, Claude; Redondo, María Julia; Solotar, Andrea

doi:10.2140/ant.2010.4.625

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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

DOI: 10.2140/ant.2010.4.625

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

Mathematical Subject Classification 2000

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

Vol. 4, No. 5, 2010