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

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.

grading, Galois covering, fundamental group
Mathematical Subject Classification 2000
Primary: 16W50
Secondary: 16S50
Received: 24 November 2009
Accepted: 1 April 2010
Published: 10 July 2010
Claude Cibils
Institut de mathématiques et de modélisation de Montpellier I3M
UMR 5149
Université Montpellier 2
F-34095 Montpellier cedex 5
María Julia Redondo
Departamento de Matemática
Universidad Nacional del Sur
Avenida Leandro N. Alem 1253
B8000CPB Bahía Blanca
Andrea Solotar
Departamento de Matemática
Facultad de Ciencias Exactas y Naturales
Universidad de Buenos Aires
Ciudad Universitaria, Pabellón 1
C1428EGA Buenos Aires