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Article contents
The Allison–Faulkner construction of 
$E_8$
Part of:
Lie algebras and Lie superalgebras
Other nonassociative rings and algebras
Linear algebraic groups and related topics
Published online by Cambridge University Press: 10 September 2021
Abstract
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.
MSC classification
Primary:
20G41: Exceptional groups
- Type
- Article
- Information
- Copyright
- © Canadian Mathematical Society 2021
Footnotes
The first author was supported by RFBR grant 19-01-00513. The second author was supported by FWO project G004018N.
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