Rigid quivers and rigid algebras

Abstract

We define a quiver to be rigid if all the associated truncated quiver algebras are rigid. The rigidity of quivers is then determined by the combinatorics of the set of pairs of parallel paths of the underlying quiver as follows from Cibils' criteria for the rigidity of truncated quiver algebras.In this paper we characterize rigid quivers Δ and relate this characterization with the condensed quiver and the quiver of beads of Δ, two much simpler quivers associated to Δ. The first one is a well-known object and the second one is introduced by us to this end.