Universal $R$--matrices for non-standard (1+1) quantum groups

Details Universal $R$--matrices for non-standard (1+1) quantum groups Universal $R$--matrices for non-standard (1+1) quantum groups

1995-01-27

arxiv.org/abs/q-alg/9501030v1

J.Phys. A28 (1995) 3129-3138

Mathematics

Quantum Algebra

12 pages, LaTeX.

Scientific paper

10.1088/0305-4470/28/11/015

A universal quasitriangular $R$--matrix for the non-standard quantum (1+1) Poincar\'e algebra $U_ziso(1,1)$ is deduced by imposing analyticity in the deformation parameter $z$. A family $g_\mu$ of ``quantum graded contractions" of the algebra $U_ziso(1,1)\oplus U_{-z}iso(1,1)$ is obtained; this set of quantum algebras contains as Hopf subalgebras with two primitive translations quantum analogues of the two dimensional Euclidean, Poincar\'e and Galilei algebras enlarged with dilations. Universal $R$--matrices for these quantum Weyl algebras and their associated quantum groups are constructed.

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