## Abstract

In paper [*] (P. Moylan: Czech. J. Phys., Vol. 47 (1997), p. 1251) we gave an explicit embedding of the three dimensional Euclidean algebra ε(2) into a quantum structure associated with U_{q}(so(2,1)). We used this embedding to construct skew symmetric representations of ε(2) out of skew symmetric representations of U_{q}(so(2, 1)). Here we consider generalizations of the results in [*] to a more complicated quantum group, which is of importance to physics. We consider U_{q}(so(3, 2)), and we show that, for a particular representation, namely the "Rac" representation, many of the results in [*] carry over to this case. In particular, we construct representations of so(3, 2), P(2, 2), the Poincaré algebra in 2+2 dimensions, and the Poincaré algebra out of the Rac representation of U_{q}(So(3, 2)). These results may be of interest to those working on exploiting representations of U_{q}(So(3, 2)), like the Rac, as an example of kinematical confinement for particle constituents such as the quarks.

Original language | English (US) |
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Pages (from-to) | 1457-1464 |

Number of pages | 8 |

Journal | Czechoslovak Journal of Physics |

Volume | 48 |

Issue number | 11 |

DOIs | |

State | Published - Nov 1998 |

## All Science Journal Classification (ASJC) codes

- General Physics and Astronomy