The normalization of the representation dimension proposed here refers to the exterior algebras Λ(V) of finite dimensional vector spaces V as the corresponding basic objects - the normalized representation dimension of Λ(V) is just the projective dimension of V. Instead of looking at the exterior algebras, one also may refer to truncated symmetric algebras, as Krause-Kussin and Oppermann have shown, or else to corresponding graded algebras (see the main examples).
Note that the reference to exterior algebras and symmetric algebras seems to be quite natural, since the new developments indicate that the representation dimension is strongly related to (twisted) commutativity conditions.