Hamiltonian lattice gravity. Deformations of discrete manifolds

The structure constants appearing in the Poisson-brackets relations among constraints in the Hamiltonian theory of gravity depend on the properties of deformations of a d-dimensional spatial manifold embedded in a (d+1)-dimensional continuum. The study of such deformations is extended to the case where the d-dimensional manifold is a piecewise flat Regge lattice. Although we cannot say whether the algebra of deformations does or does not close for the general lattice, should it close we provide a prescription for obtaining the structure constants. We discuss the case of small lattices where closure can be demonstrated explicitly.