group theory

# Contents

## Definition

The Lorentz group is the orthogonal group for an invariant bilinear form of signature $(-+++\cdots)$, $O(n,1)$.

In physics the theory of special relativity the Lorentz group acts canonically as the group of linear isometries of Minkowski spacetime preserving a chosen basepoint. This is called the action by Lorentz transformations.

groupsymboluniversal coversymbolhigher coversymbol
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)$$\,$$\,$
conformal group$\mathrm{O}(n+1,t+1)$$\,$
Narain group$O(n,n)$
Poincaré group$ISO(n,1)$Poincaré spin group$\widehat {ISO}(n,1)$$\,$$\,$
super Poincaré group$sISO(n,1)$$\,$$\,$$\,$$\,$
superconformal group

## References

Revised on March 20, 2015 13:39:27 by Urs Schreiber (80.92.246.195)