New quantum (anti)de Sitter algebras and discrete symmetries
نویسنده
چکیده
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 for time and space discrete Maxwell equations with quantum algebra symmetry.
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