nLab
SO(12)

Contents

Idea

SO(12)SO(12) is the special orthogonal group in dimension 12.

Spin(12)Spin(12) is the spin group in dimension 12.

In the classification of simple Lie groups this is the entry D6.

rotation groups in low dimensions:

Dynkin labelsp. orth. groupspin grouppin groupsemi-spin group
SO(2)Spin(2)Pin(2)
B1SO(3)Spin(3)Pin(3)
D2SO(4)Spin(4)Pin(4)
B2SO(5)Spin(5)Pin(5)
D3SO(6)Spin(6)
B3SO(7)Spin(7)
D4SO(8)Spin(8)SO(8)
B4SO(9)Spin(9)
D5SO(10)Spin(10)
B5SO(11)Spin(11)
D6SO(12)Spin(12)
\vdots\vdots
D8SO(16)Spin(16)SemiSpin(16)
\vdots\vdots
D16SO(32)Spin(32)SemiSpin(32)

see also


References

General

(…)

As a grand unified gauge group

Discussion as a gauge group in grand unified theory (see there):