The classification of orbits on certain exceptional Jordan algebra under the automorphism group

Abstract

Let ${\mathcal{J}}^1$ be the real form of complex simple Jordan algebra with the automorphism group $G$ of type $F_{4(-20)}$. Explicitly, we give the orbit decomposition of ${\mathcal{J}}^1$ under the action of $G$ and determine the Lie group structure of stabilizer for each $G$-orbit on ${\mathcal{J}}^1$.

v4, 57 pages, presentation improved, minor errors corrected and the title changed

References in corpus (1)

• Exceptional Lie groups

Cited by in corpus (1)

• The Iwasawa decomposition and the Bruhat decomposition of the automorphism group on certain exceptional Jordan algebra