Deformed Kac-Moody and Virasoro Algebras

Details Deformed Kac-Moody and Virasoro Algebras Deformed Kac-Moody and Virasoro Algebras

2006-08-12

arxiv.org/abs/hep-th/0608081v3

J.Phys.A40:7789-7802,2007

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/1751-8113/40/27/023

Whenever the group $\R^n$ acts on an algebra $\calA$, there is a method to twist $\cal A$ to a new algebra $\calA_\theta$ which depends on an antisymmetric matrix $\theta$ ($\theta^{\mu \nu}=-\theta^{\nu \mu}=\mathrm{constant}$). The Groenewold-Moyal plane $\calA_\theta(\R^{d+1})$ 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 $Q_\mu$. For $\calA_\theta(\R^{d+1})$, $Q_\mu$ 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.

Affiliated with

Also associated with

No associations

Rating

Deformed Kac-Moody and Virasoro Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Deformed Kac-Moody and Virasoro Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deformed Kac-Moody and Virasoro Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-586339