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We consider the (finite-dimensional) restricted quantum group U‾qsℓ(2) at q=i. We show that U‾isℓ(2) does not allow for a universal R-matrix, even though U⊗V≅V⊗U holds for all finite-dimensional representations U,V of U‾isℓ(2). We then give an explicit coassociator Φ and a universal R-matrix R such that U‾isℓ(2) becomes a quasi-triangular quasi-Hopf algebra.Our construction is motivated by the two-dimensional...
We describe a relationship between homological representations of the braid groups due to R. Lawrence, D. Krammer, and S. Bigelow and the monodromy representations of the Knizhnik-Zamolodchikov (KZ) connection. First, we describe the comparison theorem in the case of generic parameters. Then, we discuss the nongeneric case from the viewpoint of conformal field theory.
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