The Allison–Faulkner construction of
| Autor: | Victor Petrov, Simon W. Rigby |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Canadian Mathematical Bulletin. 65:686-701 |
| ISSN: | 1496-4287 0008-4395 |
| DOI: | 10.4153/s0008439521000813 |
| Popis: | We show that the Tits index $E_{8,1}^{133}$ cannot be obtained by means of the Tits construction over a field with no odd degree extensions. The proof uses a general method coming from the theory of symmetric spaces. We construct two cohomological invariants, in degrees $6$ and $8$ , of the Tits construction and the more symmetric Allison–Faulkner construction of Lie algebras of type $E_8$ and show that these invariants can be used to detect the isotropy rank. |
| Databáze: | OpenAIRE |
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