nLab Clifford bundle

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Contents

Ingredients

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)

A Clifford bundle is a fiber bundle of Clifford algebras.

Given a spin bundle $P$ , then the associated bundle $P \underset{Spin(n)}{\times} Cl_n$ is a Clifford bundle.

H. Blaine Lawson, Marie-Louise Michelsohn, chapter II, section 3 Spin geometry, Princeton University Press (1989)

Created on November 24, 2014 at 19:07:58. See the history of this page for a list of all contributions to it.