Deformed Kac-Moody and Virasoro Algebras

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dc.creatorBalachandran, A. P.
dc.creatorQueiroz, A. R.
dc.creatorMarques, A. M.
dc.creatorTeotonio-Sobrinho, P.
dc.date2006-08-12
dc.date2007-02-22
dc.date.accessioned2026-07-07T11:07:02Z
dc.date.available2026-07-07T11:07:02Z
dc.descriptionWhenever the group $\R^n$ acts on an algebra $\calA$, there is a method to twist $\cal A$ to a new algebra $\calA_θ$ which depends on an antisymmetric matrix $θ$ ($θ^{μν}=-θ^{νμ}=\mathrm{constant}$). The Groenewold-Moyal plane $\calA_θ(\R^{d+1})$ is an example of such a twisted algebra. We give a general construction to realise this twist in terms of $\calA$ itself and certain ``charge'' operators $Q_μ$. For $\calA_θ(\R^{d+1})$, $Q_μ$ are translation generators. This construction is then applied to twist the oscillators realising the Kac-Moody (KM) algebra as well as the KM currents. They give different deformations of the KM algebra. From one of the deformations of the KM algebra, we construct, via the Sugawara construction, the Virasoro algebra. These deformations have implication for statistics as well.
dc.descriptionFirst resubmission: Some important changes performed. Title and Abstract are changed. New references added. LateX, no figures, 18 pages. Second resubmission: small changes
dc.identifierhttps://arxiv.org/abs/hep-th/0608081
dc.identifierhttp://arxiv.org/abs/hep-th/0608081
dc.identifierJ.Phys.A40:7789-7802,2007
dc.identifierdoi:10.1088/1751-8113/40/27/023
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/189712
dc.subjectHigh Energy Physics - Theory
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectMathematical Physics
dc.subjectQuantum Algebra
dc.titleDeformed Kac-Moody and Virasoro Algebras
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