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Pré-Publication, Document De Travail Année : 2006

On Galois coverings and tilting modules

Résumé

Let A be a basic and connected finite dimensional algebra over an algebraically closed field, let G be a group, let T be a basic tilting A-module and let B the endomorphism algebra of T. We compare the set of isoclasses of Galois coverings of A with group G and the set of isoclasses of Galois coverings of B with group G. When G is finite we establish a bijection between these two sets. When G is infinite, we give sufficient conditions on T for this bijection to hold. Finally, we apply these results to study when the simple connectedness of A implies the one of B.
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Dates et versions

hal-00097962 , version 1 (22-09-2006)
hal-00097962 , version 2 (26-09-2006)
hal-00097962 , version 3 (17-11-2006)
hal-00097962 , version 4 (12-01-2007)

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Patrick Le Meur. On Galois coverings and tilting modules. 2006. ⟨hal-00097962v2⟩
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