The exceptional group <i>G</i> <sub>2</sub>

Adam M. Bincer

in Lie Groups and Lie Algebras

Published in print October 2012 | ISBN: 9780199662920
Published online January 2013 | e-ISBN: 9780191745492 | DOI:
The exceptional group G 2

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The exceptional Lie algebra G2 is obtained as a subgroup of SO(7) by making use of the octonionic habc. It is shown that G2 is the group of automorphisms of octonions O , while the corresponding groups for quaternions H is SO(3) and for the complex C, it is Z2. The group G2 was introduced into Physics by Racah in his treatment of the configuration ln for n equivalent electrons in the l shell. Biographical notes on Racah are given.

Keywords: exceptional group G2; automorphisms; octonions; equivalent electrons

Chapter.  2058 words. 

Subjects: Mathematical and Statistical Physics

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