Transformations of Bound Quivers

A quiver Q is a directed multigraph. Representations of Q are assignments of vector spaces and linear maps to the vertices and arrows of Q; these are categorically equivalent to the modules over the path algebra kQ. The indecomposable representations of a given quiver and the irreducible morphisms between them are summarized combinatorially in the Auslander-Reiten quiver which, in the case of algebras of finite representation type, gives almost complete information about the category of representations. We introduce an intuitive transformation from a family of bound quivers to a family of A-type quivers which preserves properties of the Auslander-Reiten quiver.