On the recursive construction of indecomposable quiver representations

For a fixed root of a quiver, it is a very hard problem to construct all or even only one indecomposable representation with this root as dimension vector. We investigate two methods which can be used for this purpose. In both cases we get an embedding of the category of representations of a new quiver into the category of representations of the original one which increases dimension vectors. Thus it can be used to construct indecomposable representations of the original quiver recursively. Actually, it turns out that there is a huge class of representations which can be constructed using these methods.