| On Galois coverings and tilting modules (2006) | |||||||||||||||||
Abstract | |||||||||||||||||
| 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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