Abstract
A universal quasi-triangular R-matrix for the non-standard quantum (1+1) Poincare algebra Uziso(1,1) is deduced by imposing analyticity in the deformation parameter z. A family Uwgmu of 'quantum graded contractions' of the algebra Uziso(1,1)(+)U-ziso(1,1) is obtained. Quantum analogues of the two-dimensional Euclidean, Poincare and Galilei algebras enlarged with dilations are contained in Uwgmu as Hopf subalgebras with two primitive translations. Universal R-matrices for these quantum Weyl (similitude) algebras and their associated quantum groups are constructed.