### Abstract

We make use of a well-know deformation of the Poincaré Lie algebra in p + q + 1 dimensions (p + q > 0) to construct the Poincaré Lie algebra out of the Lie algebras of the de Sitter and anti de Sitter groups, the generators of the Poincaré Lie algebra appearing as certain irrational functions of the generators of the de Sitter groups. We have obtained generalizations of this "anti-deformation" for the SO(p + 2, q) and SO(p + 1, q + 1) cases with arbitrary p and q. Similar results have been established for q deformations U_{q}(so(p, q)) with small p and q values. Combining known results on representations of U_{q}(so(p, q)) (for q both generic and a root of unity) with our "anti-deformation" formulae, we get representations of classical Lie algebras which depend upon the deformation parameter q. Explicit results are given for the simplest example (of type A_{1}) i.e. that associated with U_{q}(so(2, 1)).

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

Pages (from-to) | 683-686 |

Number of pages | 4 |

Journal | Institute of Physics Conference Series |

Volume | 173 |

State | Published - 2003 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

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*Institute of Physics Conference Series*, vol. 173, pp. 683-686.

**Representations of classical Lie algebras from their quantum deformations.** / Moylan, Patrick J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Representations of classical Lie algebras from their quantum deformations

AU - Moylan, Patrick J.

PY - 2003

Y1 - 2003

N2 - We make use of a well-know deformation of the Poincaré Lie algebra in p + q + 1 dimensions (p + q > 0) to construct the Poincaré Lie algebra out of the Lie algebras of the de Sitter and anti de Sitter groups, the generators of the Poincaré Lie algebra appearing as certain irrational functions of the generators of the de Sitter groups. We have obtained generalizations of this "anti-deformation" for the SO(p + 2, q) and SO(p + 1, q + 1) cases with arbitrary p and q. Similar results have been established for q deformations Uq(so(p, q)) with small p and q values. Combining known results on representations of Uq(so(p, q)) (for q both generic and a root of unity) with our "anti-deformation" formulae, we get representations of classical Lie algebras which depend upon the deformation parameter q. Explicit results are given for the simplest example (of type A1) i.e. that associated with Uq(so(2, 1)).

AB - We make use of a well-know deformation of the Poincaré Lie algebra in p + q + 1 dimensions (p + q > 0) to construct the Poincaré Lie algebra out of the Lie algebras of the de Sitter and anti de Sitter groups, the generators of the Poincaré Lie algebra appearing as certain irrational functions of the generators of the de Sitter groups. We have obtained generalizations of this "anti-deformation" for the SO(p + 2, q) and SO(p + 1, q + 1) cases with arbitrary p and q. Similar results have been established for q deformations Uq(so(p, q)) with small p and q values. Combining known results on representations of Uq(so(p, q)) (for q both generic and a root of unity) with our "anti-deformation" formulae, we get representations of classical Lie algebras which depend upon the deformation parameter q. Explicit results are given for the simplest example (of type A1) i.e. that associated with Uq(so(2, 1)).

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UR - http://www.scopus.com/inward/citedby.url?scp=4944232171&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:4944232171

VL - 173

SP - 683

EP - 686

JO - Institute of Physics Conference Series

JF - Institute of Physics Conference Series

SN - 0951-3248

ER -