| Galois coverings and simple connectedness of piecewise hereditary algebras (2007) | |||||||||||||||||
Abstract | |||||||||||||||||
| Let A a basic connected and finite dimensional piecewise hereditary algebra of type Q. We prove that A admits a universal Galois covering with group the fundamental group of Q. As a corollary, we deduce that A is simply connected if and only if Q is a tree, if and only if the Hocschild cohomology group HH^1(A) vanishes. As an application, we prove that if C->A is a Galois covering with group G, then C is piecewise hereditary of type a Galois covering with group G of Q. | |||||||||||||||||
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