Deformed Kac-Moody and Virasoro Algebras

Balachandran, A. P.; Queiroz, A. R.; Marques, A. M.; Teotonio-Sobrinho, P.

Deformed Kac-Moody and Virasoro Algebras

Authors

Balachandran, A. P.

Queiroz, A. R.

Marques, A. M.

Teotonio-Sobrinho, P.

Description

Whenever 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.
First resubmission: Some important changes performed. Title and Abstract are changed. New references added. LateX, no figures, 18 pages. Second resubmission: small changes