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

The Hopf algebra dual form for the non--standard uniparametric deformation of the (1+1) Poincaré algebra $iso(1,1)$ is deduced. In this framework, the quantum coordinates that generate $Fun_w(ISO(1,1))$ define an infinite dimensional Lie algebra. A change in the basis of the dual form is obtained in order to compare this deformation to the standard one. Finally, a non--standard quantum Heisenberg group acting on a quantum Galilean plane is obtained.

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