nLab Spin(11,3)

Idea

$Spin(11,3)$ denotes the spin group-cover of the Lorentz groups in signature $(11,3)$.

Related entries

• D=14 supersymmetry

• Spin(10,2)

• Spin(9,1)

rotation groups in low dimensions:

Dynkin label	sp. orth. group	spin group	pin group	semi-spin group
	SO(2)	Spin(2)	Pin(2)
B1	SO(3)	Spin(3)	Pin(3)
D2	SO(4)	Spin(4)	Pin(4)
B2	SO(5)	Spin(5)	Pin(5)
D3	SO(6)	Spin(6)
B3	SO(7)	Spin(7)
D4	SO(8)	Spin(8)		SO(8)
B4	SO(9)	Spin(9)
D5	SO(10)	Spin(10)
B5	SO(11)	Spin(11)
D6	SO(12)	Spin(12)
	$\vdots$	$\vdots$
D8	SO(16)	Spin(16)		SemiSpin(16)
	$\vdots$	$\vdots$
D16	SO(32)	Spin(32)		SemiSpin(32)

see also

• Spin(5).Spin(3)

• finite rotation groups

• ADE-classification

References

Construction via octonions and with speculations on a possible role in the standard model of particle physics:

• Kirill Krasnov, $Spin(11,3)$, particles and octonions (arXiv:2104.01786)