Matrix regularization of embedded 4-manifolds Original Research Article

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