nLab Spin(11,3)

Contents

Context

Group Theory

Spin geometry

Contents

Idea

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

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

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

Last revised on April 6, 2021 at 09:22:57. See the history of this page for a list of all contributions to it.