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-Realization of Lie Algebras: Application to so(4,2) and Algebras

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Abstract:

The property of some finite -algebras to appear as the commutant of a particular subalgebra in a simple Lie algebra is exploited for the obtention of new -realizations from a “canonical” differential one.

The method is applied to the conformal algebra so(4,2) and therefore yields also results for its Poincar\'e subalgebra. Unitary irreducible representations of these algebras are recognized in this approach, which is naturally compared -or associated- to the induced representation technique.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique {URA 14-36 du CNRS, associée à l'Ecole Normale Supérieure de Lyon et à l'Université de Savoie}, Groupe d'Annecy: LAPP, Chemin de Bellevue BP 110, F-74941 Annecy-le-Vieux Cedex, France, , , , , , FR

    F. Barbarin & E. Ragoucy

  2. Laboratoire de Physique Théorique, Groupe de Lyon: ENS Lyon, 46 allée d'Italie, F-69364 Lyon Cedex 07, France, , , , , , FR

    P. Sorba

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  1. F. Barbarin
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  2. E. Ragoucy
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  3. P. Sorba
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Received: 10 June 1996 / Accepted: 8 October 1996

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Barbarin, F., Ragoucy, E. & Sorba, P. -Realization of Lie Algebras: Application to so(4,2) and Algebras . Comm Math Phys 186, 393–411 (1997). https://doi.org/10.1007/s002200050114

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  • DOI: https://doi.org/10.1007/s002200050114

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