无双旁路三角代数的基本群
The fundamental group of a triangular algebra without double bypasses
摘要：
设A是域k上的基本连通有限维代数，Q是A的普通代数.对于A与Q的任何表示和容许关系，R。Martinez-Villa和J.A. de La Pena已经将一个称为本演示文稿的基本群的群联系起来。具有非同构基本群的A可能存在不同的表示。本文证明了：如果域k的特征为零，Q没有定向圈，Q没有双旁路，则存在A的特权表示，使得任何其它表示的基本群是这个特权表示的基本群的商.
英文摘要：
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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