Geodesic
The Allison–Faulkner construction of $E_8$
Canadian mathematical bulletin, Tome 65 (2022) no. 3, pp. 686-701

Voir la notice de l'article provenant de la source Cambridge

DOI

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.
DOI : 10.4153/S0008439521000813
Mots-clés : Exceptional algebraic groups, Tits construction, structurable algebras 
Petrov, Victor; Rigby, Simon W. The Allison–Faulkner construction of $E_8$. Canadian mathematical bulletin, Tome 65 (2022) no. 3, pp. 686-701. doi: 10.4153/S0008439521000813
@article{10_4153_S0008439521000813,
     author = {Petrov, Victor and Rigby, Simon W.},
     title = {The {Allison{\textendash}Faulkner} construction of $E_8$},
     journal = {Canadian mathematical bulletin},
     pages = {686--701},
     year = {2022},
     volume = {65},
     number = {3},
     doi = {10.4153/S0008439521000813},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439521000813/}
}
TY  - JOUR
AU  - Petrov, Victor
AU  - Rigby, Simon W.
TI  - The Allison–Faulkner construction of $E_8$
JO  - Canadian mathematical bulletin
PY  - 2022
SP  - 686
EP  - 701
VL  - 65
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008439521000813/
DO  - 10.4153/S0008439521000813
ID  - 10_4153_S0008439521000813
ER  - 
%0 Journal Article
%A Petrov, Victor
%A Rigby, Simon W.
%T The Allison–Faulkner construction of $E_8$
%J Canadian mathematical bulletin
%D 2022
%P 686-701
%V 65
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439521000813/
%R 10.4153/S0008439521000813
%F 10_4153_S0008439521000813

Cité par Sources :