Quantized $SL(2)$ representations of knot groups

Jun Murakami, Roland van der Veen

Published 2018-12-22Version 1

A quantum deformation of the space of $SL(2)$ representations of knot groups is constructed using the braided quantum group $BSL(2)$ introduced by S. Majid, which is a quantum analogue of the group $SL(2)$ obtained by quantizing the coordinate ring of $SL(2)$ and also quantizing the flip of the tensor product by changing it to a braiding. This construction works for any braided Hopf algebra satisfying braided commutativity.