The fundamental group of a triangular algebra without double bypasses
Abstract
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.
Keywords
Cite
@article{arxiv.math/0503302,
title = {The fundamental group of a triangular algebra without double bypasses},
author = {Patrick Le Meur},
journal= {arXiv preprint arXiv:math/0503302},
year = {2008}
}
Comments
The proofs of the results in this note will be given in a subsequent paper where the framework will be extended to galois coverings of an algebra