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arXiv · 1109.0975

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

Akihiro Nishio
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Abstract

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 $K_{\epsilon}-$Iwasawa decomposition, the Matsuki decomposition, and the Bruhat and Gauss decompositions.

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Akihiro Nishio. 2011-09-05. The Iwasawa decomposition and the Bruhat decomposition of the automorphism group on certain exceptional Jordan algebra. https://arxiv.org/abs/1109.0975

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