Geodesic
Order 3 Elements in G2 and Idempotents in Symmetric Composition Algebras
Canadian journal of mathematics, Tome 70 (2018) no. 5, pp. 1038-1075

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

DOI

Order three elements in the exceptional groups of type ${{G}_{2}}$ are classified up to conjugation over arbitrary fields. Their centralizers are computed, and the associated classification of idempotents in symmetric composition algebras is obtained. Idempotents have played a key role in the study and classification of these algebras.Over an algebraically closed field, there are two conjugacy classes of order three elements in ${{G}_{2}}$ in characteristic not 3 and four of them in characteristic 3. The centralizers in characteristic 3 fail to be smooth for one of these classes.
DOI : 10.4153/CJM-2017-039-6
Mots-clés : 17A75, 14L15, 17B25, 20G15, symmetric composition algebra, Okubo algebra, automorphism group, centralizer, idempotent 
Elduque, Alberto. Order 3 Elements in G2 and Idempotents in Symmetric Composition Algebras. Canadian journal of mathematics, Tome 70 (2018) no. 5, pp. 1038-1075. doi: 10.4153/CJM-2017-039-6
@article{10_4153_CJM_2017_039_6,
     author = {Elduque, Alberto},
     title = {Order 3 {Elements} in {G2} and {Idempotents} in {Symmetric} {Composition} {Algebras}},
     journal = {Canadian journal of mathematics},
     pages = {1038--1075},
     year = {2018},
     volume = {70},
     number = {5},
     doi = {10.4153/CJM-2017-039-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-039-6/}
}
TY  - JOUR
AU  - Elduque, Alberto
TI  - Order 3 Elements in G2 and Idempotents in Symmetric Composition Algebras
JO  - Canadian journal of mathematics
PY  - 2018
SP  - 1038
EP  - 1075
VL  - 70
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-039-6/
DO  - 10.4153/CJM-2017-039-6
ID  - 10_4153_CJM_2017_039_6
ER  - 
%0 Journal Article
%A Elduque, Alberto
%T Order 3 Elements in G2 and Idempotents in Symmetric Composition Algebras
%J Canadian journal of mathematics
%D 2018
%P 1038-1075
%V 70
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-039-6/
%R 10.4153/CJM-2017-039-6
%F 10_4153_CJM_2017_039_6

Cité par Sources :