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.

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

References in corpus (1)

• The Lie algebra structure on the first Hochschild cohomology group of a monomial algebra

Cited by in corpus (7)

• The universal cover of an algebra without double bypass
• The Intrinsic Fundamental Group of a Linear Category
• Gradings, smash products and Galois coverings of a small category
• On maximal diagonalizable Lie subalgebras of the first Hochschild cohomology
• On Galois coverings and tilting modules
• The universal cover of a monomial triangular algebra without multiple arrows
• On universal gradings, versal gradings and Schurian generated categories