nLab
super Poincaré group

Idea

The super Poincaré group is the Lie integration in supergeometry of the super Poincaré Lie algebra. This is a super-extension of the ordinary Poincaré group.

Related concepts

• Poincaré group

• super Poincaré Lie algebra

• super translation algebra

• unitary representation of the super Poincaré group

group	symbol	universal cover	symbol	higher cover	symbol
orthogonal group	$\mathrm{O}(n)$	Pin group	$\mathrm{Pin}(n)$	Tring group	$\mathrm{Tring}(n)$
special orthogonal group	$\mathrm{SO}(n)$	Spin group	$\mathrm{Spin}(n)$	String group	$\mathrm{String}(n)$
Lorentz group	$\mathrm{O}(n,1)$	$$	$\mathrm{Spin}(n,1)$	$$	$$
anti de Sitter group	$\mathrm{O}(n,2)$	$$	$\mathrm{Spin}(n,2)$	$$	$$
Narain group	$O(n,n)$
Poincaré group	$\mathrm{ISO}(n,1)$	$$	$$	$$	$$
super Poincaré group	$\mathrm{sISO}(n,1)$	$$	$$	$$	$$

References

• Super spacetimes and super Poincaré-group (pdf)