Using recent results on string on $AdS_{3}\times N^d$, where N is ad-dimensional compact manifold, we re-examine the derivation of the non trivialextension of the (1+2) dimensional-Poincar\'e algebra obtained by Rausch deTraubenberg and Slupinsky, refs [1] and [29]. We show by explicit computationthat this new extension is a special kind of fractional supersymmetric algebrawhich may be derived from the deformation of the conformal structure living onthe boundary of $AdS_3$. The two so(1,2) Lorentz modules of spin $\pm{1\overk}$ used in building of the generalisation of the (1+2) Poincar\'e algebra arere-interpreted in our analysis as highest weight representations of the leftand right Virasoro symmetries on the boundary of $AdS_3$. We also completeknown results on 2d-fractional supersymmetry by using spectral flow of affineKac-Moody and superconformal symmetries. Finally we make preliminary commentson the trick of introducing Fth-roots of g-modules to generalise the so(1,2)result to higher rank lie algebras g.
展开▼
机译：使用$ AdS_ {3} \ times N ^ d $上字符串的最新结果，其中N是广告维紧流形，我们重新检查（1 + 2）维-庞加莱的非trivialextension的推导Rausch deTraubenberg和Slupinsky获得的代数，参考文献[1]和[29]。通过显式计算，我们证明了这一新扩展是分数超对称代数的一种特殊形式，它可以源自生活在$ AdS_3 $边界上的共形结构的变形。在分析（1 + 2）庞加莱代数的泛化中使用的自旋$ \ pm {1 \ overk} $的两个so（1,2）Lorentz模块在我们的分析中被重新解释为的最高权重表示$ AdS_3 $边界上的左右Virasoro对称性。我们还使用仿射Kac-Moody的频谱流和超共形对称性完成了二维分数超对称性的已知结果。最后，我们对引入g-模块的Fth根以将so（1,2）结果推广到更高阶的李代数g的技巧进行初步评论。
展开▼
