Quasitriangular structure and twisting of the 2+1 bicrossproduct model

Abstract

We show that the bicrossproduct model $C[S{U}_2^{\ast }]▶◃U(s{u}_2)$ quantum Poincare group in 2+1 dimensions acting on the quantum spacetime $[x_i,t]=ı\lambda x_i$ is related by a Drinfeld and module-algebra twist to the quantum double $U(s{u}_2)⋉C[S{U}_2]$ acting on the quantum spacetime $[x_{\mu },x_{\nu }]=ı\lambda {\epsilon }_{\mu \nu \rho }{x}_{\rho }$. We obtain this twist by taking a scaling limit as $q\to 1$ 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.

27 pages latex

References in corpus (1)

• Generalised Chern-Simons actions for 3d gravity and kappa-Poincare symmetry

Cited by in corpus (2)

• Quantum gravity on a square graph
• On the emergence of the structure of Physics