Abstract
Two new quantum deformations of the Lie algebras so(4,2) and so(5,1) are constructed as quantum conformal algebras of the Minkowskian and Euclidean spaces. These deformations are called either ‘mass-like’ or ‘length-like’ 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 to new quantum conformal Galilean algebras. These quantum conformal 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 for time and space discrete Maxwell equations with quantum algebra symmetry.
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