### Abstract

We show that it is possible to express the basis elements of the Lie algebra of the Euclidean group, E(2), as simple irrational functions of certain q deformed expressions involving the generators of the quantum algebra U_{q}(so(2, 1)). We consider implications of these results for the representation theory of the Lie algebra of E(2). We briefly discuss analogous results for U_{q}(so(2, 2)).

Original language | English (US) |
---|---|

Pages (from-to) | 1251-1258 |

Number of pages | 8 |

Journal | Czechoslovak Journal of Physics |

Volume | 47 |

Issue number | 12 |

DOIs | |

State | Published - Jan 1 1997 |

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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. 47, no. 12, pp. 1251-1258. https://doi.org/10.1023/A:1022829700566

**Embedding Euclidean Lie algebras into quantum structures.** / Moylan, Patrick J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Embedding Euclidean Lie algebras into quantum structures

AU - Moylan, Patrick J.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - We show that it is possible to express the basis elements of the Lie algebra of the Euclidean group, E(2), as simple irrational functions of certain q deformed expressions involving the generators of the quantum algebra Uq(so(2, 1)). We consider implications of these results for the representation theory of the Lie algebra of E(2). We briefly discuss analogous results for Uq(so(2, 2)).

AB - We show that it is possible to express the basis elements of the Lie algebra of the Euclidean group, E(2), as simple irrational functions of certain q deformed expressions involving the generators of the quantum algebra Uq(so(2, 1)). We consider implications of these results for the representation theory of the Lie algebra of E(2). We briefly discuss analogous results for Uq(so(2, 2)).

UR - http://www.scopus.com/inward/record.url?scp=0031316056&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031316056&partnerID=8YFLogxK

U2 - 10.1023/A:1022829700566

DO - 10.1023/A:1022829700566

M3 - Article

AN - SCOPUS:0031316056

VL - 47

SP - 1251

EP - 1258

JO - Czechoslovak Journal of Physics

JF - Czechoslovak Journal of Physics

SN - 0011-4626

IS - 12

ER -