  We study the generalization of the idea of a local quiver of a representation
of a formally smooth algebra, to broader classes of finitely generated
algebras. In this new setting we can construct for every semisimple
representation $M$ a local model and a non-commutative tangent cone. The
representation schemes of these new algebras model the local structure and the
tangent cone of the representation scheme of the original algebra at $M$. In
this way one can try to classify algebras according to their local behavior. As
an application we will show that the tangent cones of Calabi Yau 2 Algebras are
always preprojective algebras. For Calabi Yau 3 Algebras the corresponding
statement would be that the local model and the tangent cones derive from
superpotentials. Although we do not have a proof in all cases, we will show
that this will indeed hold in many cases.
