Representations of Quivers

Abstract

A quiver is a finite directed graph. The associated path algebra has all paths of the quiver as a basis, and the multiplication is defined in terms of concatenating paths when possible. We have seen representations of a quiver earlier, and we also have seen how to relate representations of a quiver to modules for its path algebra. In this chapter we develop the theory further and study representations of quivers in detail. In particular we show how to exploit properties which come from the graph structure of the quiver.