Order 3 elements in G2 and idempotents in symmetric composition algebras
Rings and Algebras
2019-08-15 v1 Group Theory
Abstract
Order three elements in the exceptional groups of type G2 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 G2 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.
Keywords
Cite
@article{arxiv.1705.01293,
title = {Order 3 elements in G2 and idempotents in symmetric composition algebras},
author = {Alberto Elduque},
journal= {arXiv preprint arXiv:1705.01293},
year = {2019}
}
Comments
33 pages