arXiv subjects

Akihiro Nishio

Publications and source records attributed to Akihiro Nishio.

3 recordsLinked to original sources

arXiv2013

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

Let $\mathcal{J}^1$ be the real form of a complex simple Jordan algebra such that the automorphism group is $\mathrm{F}_{4(-20)}$. By using some orbit types of $\mathrm{F}_{4(-20)}$ on $\mathcal{J}^1$, for $\mathrm{F}_{4(-20)}$, explicitly, we give the Iwasawa decomposition, the Oshima--Sekiguchi's $K_ε-$Iwasawa decomposition, the Matsuki decomposition, and the Bruhat and Gauss decompositions.

math.DG↗

arXiv2012

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

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 $\mathcal{J}^1$.

math.DG↗

arXiv2011

Orbit decomposition of Jordan matrix algebras of order three under the automorphism groups

The orbit decomposition is given under the automorphism group on the real split Jordan algebra of all hermitian matrices of order three corresponding to any real split composition algebra, or the automorphism group on the complexification, explicitly, in terms of the cross product of H. Freudenthal and the characteristic polynomial.

math.DG↗