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There are only two quantum group structures on the space of two by two
unimodular matrices, these are the $\text{SL}_q(2)$
and the $\text{SL}_h(2)$ quantum groups.
The differential geometry of $\text{SL}_q(2)$
is well known. In this Letter, we
develop the differential geometry of $\text{SL}_h(2)$, and show that the space
of left invariant vector fields is three-dimensional.
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