Braided Momentum Structure of the q-Poincare Group

Details Braided Momentum Structure of the q-Poincare Group Braided Momentum Structure of the q-Poincare Group

1992-10-27

arxiv.org/abs/hep-th/9210141v1

J.Math.Phys. 34 (1993) 2045-2058

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, LATEX

Scientific paper

10.1063/1.530154

The $q$-Poincar\'e group of \cite{SWW:inh} is shown to have the structure of a semidirect product and coproduct $B\cocross \widetilde{SO_q(1,3)}$ where $B$ is a braided-quantum group structure on the $q$-Minkowski space of 4-momentum with braided-coproduct $\und\Delta \vecp=\vecp\tens 1+1\tens \vecp$. Here the necessary $B$ is not a usual kind of quantum group, but one with braid statistics. Similar braided-vectors and covectors $V(R')$, $V^*(R')$ exist for a general R-matrix. The abstract structure of the $q$-Lorentz group is also studied.

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