Chapter

The center and outer automorphisms of <i>Spin(n</i>)

Adam M. Bincer

in Lie Groups and Lie Algebras

Published in print October 2012 | ISBN: 9780199662920
Published online January 2013 | e-ISBN: 9780191745492 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199662920.003.0008
The center and outer automorphisms of Spin(n)

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Center and inner and outer automorphisms are defined. The chapter shows that the center of Spin(n) consists of two elements for n odd, and 4 elements for n even. More precisely the center has the structure of Z 2, Z 4 and Z 2xZ 2 for Spin(4m±1), Spin(4m+2) and Spin(4m), respectively. The chapter also shows that reflections are an outer automorphism for Spin(n) for n even, under which the two semispinors are exchanged. For n odd reflections are an inner automorphism and therefore trivial. Biographical notes on Dynkin are given.

Keywords: center; inner and outer automorphism; semispinor

Chapter.  2252 words. 

Subjects: Mathematical and Statistical Physics

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