Eur. Phys. J. C 21, 735-747 (2001)
DOI: 10.1007/s100520100769
Non-trivial extension of the (1+2)-Poincaré algebra and conformal invariance on the boundary of AdS3
I. Benkaddour, A. El Rhalami and E.H. SaidiLab/UFR High Energy Physics, Physics Department, Faculty of Science, Av. Ibn Battota, B.P. 1014, Rabat, Morocco
(Received: 20 July 2000 / Published online: 19 September 2001 -© Springer-Verlag / Società Italiana di Fisica 2001 )
Abstract
Using recent results on strings on AdS
, where
N is a
d dimensional compact manifold, we re-examine the derivation
of the
non-trivial extension of the (1+2)-dimensional-Poincaré algebra
obtained
by Rausch de Traubenberg and Slupinsky. We
show by
explicit computation that this new extension is a special kind
of
fractional supersymmetric algebra which may be derived from the
deformation of the conformal structure living on the boundary
of
AdS3. The two so(1,2) Lorentz modules of spin 
used in building of the generalization of the (1+2) Poincaré
algebra are re-interpreted in our analysis as highest weight
representations of the left and right Virasoro symmetries on
the
boundary of AdS3. We also complete known results on
2d-fractional supersymmetry by using spectral flow of
affine Kac-Moody and superconformal symmetries. Finally we make
preliminary comments on
the trick of introducing Fth roots of g-modules to generalize
the so(1,2) result to higher rank Lie algebras g.
© Società Italiana di Fisica, Springer-Verlag 2001
