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Composition algebras and the two faces of G2

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Boya, Luis J. and Campoamor Stursberg, Otto Ruttwig (2010) Composition algebras and the two faces of G2. International Journal of Geometric Methods in Modern Physics, 7 (3). pp. 367-378. ISSN 0219-8878

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Official URL: http://www.worldscientific.com/doi/abs/10.1142/S0219887810004348




Abstract

We consider composition and division algebras over the real numbers: We note two roles for the group G2: as automorphism group of the octonions and as the isotropy group of a generic 3-form in 7 dimensions. We show why they are equivalent, by means of a regular metric. We express in some diagrams the relation between some pertinent groups, most of them related to the octonions. Some applications to physics are also discussed.


Item Type:Article
Uncontrolled Keywords:First exceptional Lie group G2; composition algebra; division algebra; octonions;automorphism group of octonions; isotropy group; quaternions; split octonions; tensors; spin groups; F4
Subjects:Sciences > Mathematics > Algebra
ID Code:20883
Deposited On:17 Apr 2013 12:59
Last Modified:12 Dec 2018 15:13

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