table of orthogonal groups and related

group | symbol | universal cover | symbol | higher cover | symbol |
---|---|---|---|---|---|

orthogonal group | $\mathrm{O}(n)$ | Pin group | $Pin(n)$ | Tring group | $Tring(n)$ |

special orthogonal group | $SO(n)$ | Spin group | $Spin(n)$ | String group | $String(n)$ |

Lorentz group | $\mathrm{O}(n,1)$ | $\,$ | $Spin(n,1)$ | $\,$ | $\,$ |

anti de Sitter group | $\mathrm{O}(n,2)$ | $\,$ | $Spin(n,2)$ | $\,$ | $\,$ |

Narain group | $O(n,n)$ | ||||

PoincarĂ© group | $ISO(n,1)$ | PoincarĂ© spin group | $\widehat {ISO}(n,1)$ | $\,$ | $\,$ |

super PoincarĂ© group | $sISO(n,1)$ | $\,$ | $\,$ | $\,$ | $\,$ |

Revised on August 17, 2014 22:40:09
by Urs Schreiber
(89.204.138.55)