1995/03/23 by Shahn Majid, S. Majid, Majid, S.
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #math.QA #q-alg
paper · pdf · doi:10.48550/arxiv.q-alg/9503014
LATEX 56 pages and two figures
arxiv created 1995/03/23 · arxiv updated 2009/11/30
We use braided groups to introduce a theory of *-structures on general inhomogeneous quantum groups, which we formulate as \em quasi-* Hopf algebras. This allows the construction of the tensor product of unitary representations up to a quantum cocycle isomorphism, which is a novel feature of the inhomogeneous case. Examples include q-Poincaré quantum group enveloping algebras in R-matrix form appropriate to the previous q-Euclidean and q-Minkowski spacetime algebras R21x1x2=x2x1R and R21u1Ru2=u2R21u1R. We obtain unitarity of the fundamental differential representations. We show further that the Euclidean and Minkowski Poincaré quantum groups are twisting equivalent by a another quantum cocycle.