Braided Momentum Structure of the q-Poincare Group

Abstract

The $q$-Poincaré 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 $\undΔ\vecp=\vecp\tens 1+1\tens \vecp$. Here the necessary $B$ is not a usual kind of quantum group, but one with braid statistics. Similar braided-vectors and covectors $V(R^{\prime })$, $V^{\ast }(R^{\prime })$ exist for a general R-matrix. The abstract structure of the $q$-Lorentz group is also studied.

22 pages, LATEX

References in corpus (2)

• Quantum and Braided Linear Algebra
• The Quantum Double as Quantum Mechanics

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