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# Is there a q-analog to the braid group?

The braid group $B_n$ on $n$ strands fits into a short exact sequence of groups:

$$1 \longrightarrow P_n \longrightarrow B_n \longrightarrow S_n \longrightarrow 1,$$

where $S_n$ is the symmetric group on the strands, and $P_n$ is the normal subgroup of braids that do not permute the strands.

Since symmetric groups are, in some sense, general linear groups over the field with one element,'' perhaps there is some corresponding short exact sequence ending with $GL_n(F_q)$ that specializes to the exact sequence above as $q \rightarrow 1$.

In the spirit of the exact sequence above, is there a $q$-analog to the braid group?