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The Hopf algebra dual form for the non--standard uniparametric deformation ofthe (1+1) Poincar\'e algebra $iso(1,1)$ is deduced. In this framework, thequantum coordinates that generate $Fun_w(ISO(1,1))$ define an infinitedimensional Lie algebra. A change in the basis of the dual form is obtained inorder to compare this deformation to the standard one. Finally, a non--standardquantum Heisenberg group acting on a quantum Galilean plane is obtained.Comment: 17 pages, LaTeX

Non-standard quantum (1+1) Poincare group: a T-matrix approach