Twist maps for non-standard quantum algebras and discrete Schrodinger symmetries

Details Twist maps for non-standard quantum algebras and discrete Schrodinger symmetries Twist maps for non-standard quantum algebras and discrete Schrodinger symmetries

2000-07-05

arxiv.org/abs/math/0007020v1

J. Phys. A 33, (2000) 4859-4870

Mathematics

Quantum Algebra

16 pages, LaTeX

Scientific paper

10.1088/0305-4470/33/27/303

The minimal twist map introduced by B. Abdesselam, A. Chakrabarti, R. Chakrabarti and J. Segar (Mod. Phys. Lett. A 14 (1999) 765) for the non-standard (Jordanian) quantum sl(2,R) algebra is used to construct the twist maps for two different non-standard quantum deformations of the (1+1) Schrodinger algebra. Such deformations are, respectively, the symmetry algebras of a space and a time uniform lattice discretization of the (1+1) free Schrodinger equation. It is shown that the corresponding twist maps connect the usual Lie symmetry approach to these discrete equations with non-standard quantum deformations. This relationship leads to a clear interpretation of the deformation parameter as the step of the uniform (space or time) lattice.

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