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New time-type and space-type non-standard quantum algebras and discrete symmetries

Francisco J. Herranz
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Abstract

Starting from the classical r-matrix of the non-standard (or Jordanian) quantum deformation of the sl(2,R) algebra, new triangular quantum deformations for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously constructed by using a graded contraction scheme; these are realized as deformations of conformal algebras of (1+1)-dimensional spacetimes. Time-type and space-type quantum algebras are considered according to the generator that remains primitive after deformation: either the time or the space translation, respectively. Furthermore by introducing differential-difference conformal realizations, these families of quantum algebras are shown to be the symmetry algebras of either a time or a space discretization of (1+1)-dimensional (wave and Laplace) equations on uniform lattices; the relationship with the known Lie symmetry approach to these discrete equations is established by means of twist maps.

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BibTeXRIS

Francisco J. Herranz. 2000-09-05. New time-type and space-type non-standard quantum algebras and discrete symmetries. https://doi.org/10.1088/0305-4470%2F33%2F46%2F305

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