1 results
The Allison–Faulkner construction of
$E_8$
- Part of
-
- Journal:
- Canadian Mathematical Bulletin / Volume 65 / Issue 3 / September 2022
- Published online by Cambridge University Press:
- 10 September 2021, pp. 686-701
- Print publication:
- September 2022
-
- Article
- Export citation
-
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.
