QUASI-ASTERISK STRUCTURE ON Q-POINCARE ALGEBRAS

We use braided groups to introduce a theory of -structures on general inhomogeneous quantum groups, which we formulate as quasi- Hopf alge bras. This allows the construction of the tensor product of unitary re presentations up to a quantum cocycle isomorphism, which is a novel fe ature of the inhomogeneous case. Examples include q-Poincare quantum g roup enveloping algebras in R-matrix form appropriate to the previous q-Euclidean and q-Minkowski space-time algebras R(21)x(1)x(2) = x(2)x( 1)R and R(21)u(1)Ru(2) = u(2)R(21)u(1)R. We obtain unitarity of the fu ndamental differential representations. We further show that the Eucli dean and Minkowski-Poincare quantum groups are twisting equivalent by another quantum cocycle.