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

A universal quasitriangular $R$--matrix for the non-standard quantum (1+1) Poincaré algebra $U_ziso(1,1)$ is deduced by imposing analyticity in the deformation parameter $z$. A family $g_μ$ 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, Poincaré 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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