### 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) |
---|---|

Pages (from-to) | 1457-1464 |

Number of pages | 8 |

Journal | Czechoslovak Journal of Physics |

Volume | 48 |

Issue number | 11 |

DOIs | |

State | Published - Jan 1 1998 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

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*Czechoslovak Journal of Physics*, vol. 48, no. 11, pp. 1457-1464. https://doi.org/10.1023/A:1021625810591

**Representations of Lie algebras from representations of quantum groups.** / Moylan, Patrick J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Representations of Lie algebras from representations of quantum groups

AU - Moylan, Patrick J.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - 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 Uq(so(2,1)). We used this embedding to construct skew symmetric representations of ε(2) out of skew symmetric representations of Uq(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 Uq(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 Uq(So(3, 2)). These results may be of interest to those working on exploiting representations of Uq(So(3, 2)), like the Rac, as an example of kinematical confinement for particle constituents such as the quarks.

AB - 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 Uq(so(2,1)). We used this embedding to construct skew symmetric representations of ε(2) out of skew symmetric representations of Uq(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 Uq(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 Uq(So(3, 2)). These results may be of interest to those working on exploiting representations of Uq(So(3, 2)), like the Rac, as an example of kinematical confinement for particle constituents such as the quarks.

UR - http://www.scopus.com/inward/record.url?scp=0032244598&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032244598&partnerID=8YFLogxK

U2 - 10.1023/A:1021625810591

DO - 10.1023/A:1021625810591

M3 - Article

VL - 48

SP - 1457

EP - 1464

JO - Czechoslovak Journal of Physics

JF - Czechoslovak Journal of Physics

SN - 0011-4626

IS - 11

ER -