The fundamental group of a triangular algebra without double bypasses

Details The fundamental group of a triangular algebra without double bypasses The fundamental group of a triangular algebra without double bypasses

2005-03-15

arxiv.org/abs/math/0503302v3

Comptes Rendus de l'Academie des Sciences. Serie 1, Mathematique 341, 4 (2005) 211--216

Mathematics

Representation Theory

The proofs of the results in this note will be given in a subsequent paper where the framework will be extended to galois cove

Scientific paper

10.1016/j.crma.2005.07.004

Let A be a basic connected finite dimensional algebra over a field k and let Q be the ordinary quiver of A. To any presentation of A with Q and admissible relations, R. Martinez-Villa and J. A. de La Pena have associated a group called the fundamental group of this presentation. There may exist different presentations of A with non isomorphic fundamental groups. In this note, we show that if the field k has characteristic zero, if Q has no oriented cycles and if Q has no double bypasses then there exists a privileged presentation of A such that the fundamental group of any other presentation is the quotient of the fundamental group of this privileged presentation.

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