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Contracting the $h$-deformation of $\text{SL}(2,\Bbb{R})$, we construct a new
deformation of two-dimensional Poincar$\acute{\text{e}}$ algebra, the algebra
of functions on its group and its differential structure. It is seen that these
dual Hopf algebras are isomorphic to each other. It is also shown that the Hopf
algebra is triangular, and its universal R-matrix is also constructed
explicitly. We then find a deformation map for the universal enveloping
algebra, and at the end, give the deformed mass shells and
Lorentz transformation.
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