Quasitriangular structure and twisting of the 3D bicrossproduct model

Abstract

We show that the bicrossproduct model C[SU2∗] ▶ ◁ U (su2) quantum Poincaré group in 2+1 dimensions acting on the quantum spacetime [xi, t] = ıλxi is related by a Drinfeld and module-algebra twist to the quantum double U (su2)⊲<C[SU2] acting on the quantum spacetime [xμ, xν] = ıλϵμνρxρ. We obtain this twist by taking a scaling limit as q → 1 of the q-deformed version of the above, where it corresponds to a previous theory of q-deformed Wick rotation from q-Euclidean to q-Minkowski space. We also recover the twist result at the Lie bialgebra level.