Structurable Algebras and Groups of Type E6 and E7
| Autor: | R. Skip Garibaldi |
|---|---|
| Jazyk: | angličtina |
| Předmět: |
Discrete mathematics
Classical group Pure mathematics Jordan algebra Algebra and Number Theory Mathematics::Rings and Algebras Mathematics - Rings and Algebras Sporadic group Ree group Representation theory 17A30 (Primary) 11E72 14L30 17A40 17B25 17C30 20G15 (Secondary) Mathematics - Algebraic Geometry Mathematics::Group Theory Group of Lie type Rings and Algebras (math.RA) FOS: Mathematics Building (B N) pair Mathematics::Representation Theory Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Journal of Algebra. (2):651-691 |
| ISSN: | 0021-8693 |
| DOI: | 10.1006/jabr.2000.8514 |
| Popis: | It is well-known that every algebraic group of type F_4 is the automorphism group of an exceptional Jordan algebra, and that up to isogeny all groups of type ^1E_6 with trivial Tits algebras arise as the isometry groups of norm forms of such Jordan algebras. We describe a similar relationship between groups of type E_6 and groups of type E_7 and use it to give explicit descriptions of the homogeneous projective varieties associated to groups of type E_7 with trivial Tits algebras. The underlying algebraic structure for the relationship considered here are a sort of 56-dimensional structurable algebra which are forms of an algebra constructed from an exceptional Jordan algebra. Comment: 35 pages, AMSLaTeX -- error in final section corrected |
| Databáze: | OpenAIRE |
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