nLab
anti de Sitter group

Contents

Idea

The isometry group O(n,2)O(n,2) of (n+1)(n+1)-dimensional anti de Sitter spacetime.

Properties

Exceptional isomorphisms

  • SO(6,2)SO(4,)SO(6,2) \simeq SO(4,\mathbb{H}) (where \mathbb{H} is the quaternions)
groupsymboluniversal coversymbolhigher coversymbol
orthogonal groupO(n)\mathrm{O}(n)Pin groupPin(n)Pin(n)Tring groupTring(n)Tring(n)
special orthogonal groupSO(n)SO(n)Spin groupSpin(n)Spin(n)String groupString(n)String(n)
Lorentz groupO(n,1)\mathrm{O}(n,1)\,Spin(n,1)Spin(n,1)\,\,
anti de Sitter groupO(n,2)\mathrm{O}(n,2)\,Spin(n,2)Spin(n,2)\,\,
Narain groupO(n,n)O(n,n)
Poincaré groupISO(n,1)ISO(n,1)Poincaré spin groupISO^(n,1)\widehat {ISO}(n,1)\,\,
super Poincaré groupsISO(n,1)sISO(n,1)\,\,\,\,
Revised on October 15, 2011 03:14:19 by Urs Schreiber (82.113.99.46)