Composition algebras and the two faces of G2
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 th...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2010 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/43761 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/43761 |
| Access Level: | acceso abierto |
| Palavra-chave: | 512 First exceptional Lie group G2 Composition algebra Division algebra Octonions Automorphism group of octonions Isotropy group Quaternions Split octonions Tensors Spin groups F4 Álgebra 1201 Álgebra |
| Resumo: | 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. |
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