Extended strings and admissible words (Q1081674)

Let \(\Gamma\) be the quiver with a single vertex and m arrows, \(m\geq 2\). Let A be the path algebra of \(\Gamma\) over an algebraically closed field k. Let I(a) denote the injective representation with socle given by the simple representation S(a) of \(\Gamma\) which replaces the vertex of \(\Gamma\) by the field k and each arrow by the 0 morphism. The author begins the study of I(a) by demonstrating its great complexity.