Quantized representations of knot groups

Abstract

For a braided Hopf algebra A with braided commutativity, we introduce the space of A representations of a knot K as a generalization of the G representation space of K defined for a group G. By rebuilding the G representation space from the view point of Hopf algebras, it is extended to any braided Hopf algebra with braided commutativity. Applying this theory to BSL(2) which is the braided quantum SL(2) introduced by S. Majid, we get the space of BSL(2) representations. It is a non-commutative algebraic scheme which provides quantized SL(2) representations of K.