Representations of Lie algebras from representations of quantum groups

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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 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.

Original languageEnglish (US)
Pages (from-to)1457-1464
Number of pages8
JournalCzechoslovak Journal of Physics
Volume48
Issue number11
DOIs
StatePublished - Jan 1 1998

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algebra
embedding
quarks
physics

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

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title = "Representations of Lie algebras from representations of quantum groups",
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 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 Poincar{\'e} algebra in 2+2 dimensions, and the Poincar{\'e} 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.",
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Representations of Lie algebras from representations of quantum groups. / Moylan, Patrick J.

In: Czechoslovak Journal of Physics, Vol. 48, No. 11, 01.01.1998, p. 1457-1464.

Research output: Contribution to journalArticle

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