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)

Show Summary Details

Preview

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

Full text: subscription required

How to subscribe Recommend to my Librarian

Buy this work at Oxford University Press »

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.