COMPOSITION ALGEBRAS AND THE TWO FACES OF G₂

DOI10.1142/S0219887810004348zbMATH Open1196.22008arXiv0911.3387OpenAlexW3105703286WikidataQ58324969 ScholiaQ58324969MaRDI QIDQ3569290

L. J. Boya, Otto Rutwig Campoamor-Stursberg

Publication date: 18 June 2010

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Abstract: We consider composition and division algebras over the real numbers: We note two r^oles for the group

G_{2}

: 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.

Full work available at URL: https://arxiv.org/abs/0911.3387

zbMATH Keywords

quaternions octonions spin groups composition algebra isotropy group tensors division algebra \(F_4\)split octonions automorphism group of octonions first exceptional Lie group \(G_2\)

Mathematics Subject Classification ID

Lie algebras of Lie groups (22E60) Composition algebras (17A75) Nonassociative division algebras (17A35)

Cites Work

COMPOSITION ALGEBRAS AND THE TWO FACES OF G2

COMPOSITION ALGEBRAS AND THE TWO FACES OF G₂