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Quantum de Rham complexes on the quantum plane and the quantum group itself are
constructed for the nonstandard deformation of Fun(SL(2)). It is shown that in
contrast to the standard $q$-deformation of SL(2), the above complexes are
unique for $\text{SL}_h(2)$. Also, as a byproduct, a new deformation of the
two-dimensional Heisenberg algebra is obtained which can be used to construct
models of $h$-deformed quantum mechanics.
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