nLab
Pin(3)

Contents

Context

Group Theory

Spin geometry

Contents

Idea

The pin group in dimension 3.

Properties

Pin +(3)SO(3)×C 4Pin_+(3) \simeq SO(3) \times C_4 and Pin (3)SU(2)×C 2Pin_-(3) \simeq SU(2) \times C_2.

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

Created on August 22, 2019 at 09:51:40. See the history of this page for a list of all contributions to it.