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Starting from the classical r-matrix of the non-standard (or Jordanian)quantum deformation of the sl(2,R) algebra, new triangular quantum deformationsfor the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneouslyconstructed by using a graded contraction scheme; these are realized asdeformations of conformal algebras of (1+1)-dimensional spacetimes. Time-typeand space-type quantum algebras are considered according to the generator thatremains primitive after deformation: either the time or the space translation,respectively. Furthermore by introducing differential-difference conformalrealizations, these families of quantum algebras are shown to be the symmetryalgebras of either a time or a space discretization of (1+1)-dimensional (waveand Laplace) equations on uniform lattices; the relationship with the known Liesymmetry approach to these discrete equations is established by means of twistmaps.Comment: 17 pages, LaTe

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