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

A. Ballesteros·F. J. Herranz·J. Negro·L. M. Nieto
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Abstract

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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A. Ballesteros, F. J. Herranz, J. Negro, L. M. Nieto. 2000-07-05. Twist maps for non-standard quantum algebras and discrete Schrodinger symmetries. https://doi.org/10.1088/0305-4470%2F33%2F27%2F303

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