Abstract:For a fixed finite dimensional algebra $A$, we study full representation embeddings of the form $mod(B)\longrightarrow mod(A)$. Such an embedding is called homological, if it induces an isomorphism on all $Ext$-groups and weakly homological, if only $Ext^1$ is preserved. In case $A$ is a preprojective algebra of Dynkin type, we give an explicit classification of all weakly homological and homological embeddings.