  Two new quantum anti-de Sitter so(4,2) and de Sitter so(5,1) algebras are
presented. These deformations are called either time-type or space-type
according to the dimensional properties of the deformation parameter. Their
Hopf structure, universal R matrix and differential-difference realization are
obtained in a unified setting by considering a contraction parameter related to
the speed of light, which ensures a well defined non-relativistic limit. Such
quantum algebras are shown to be symmetry algebras of either time or space
discretizations of wave/Laplace equations on uniform lattices. These results
lead to a proposal fortime and space discrete Maxwell equations with quantum
algebra symmetry.
