  We consider products of two 2-manifolds such as S^2 x S^2, embedded in
Euclidean space and show that the corresponding 4-volume preserving
diffeomorphism algebra can be approximated by a tensor product SU(N)xSU(N) i.e.
functions on a manifold are approximated by the Kronecker product of two SU(N)
matrices. A regularization of the 4-sphere is also performed by constructing
N^2 x N^2 matrix representations of the 4-algebra (and as a byproduct of the
3-algebra which makes the regularization of S^3 also possible).
