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

DOI10.21099/TKBJM/1373893407zbMATH Open1364.17029arXiv1109.0975OpenAlexW2963156155MaRDI QIDQ357447

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Publication date: 30 July 2013

Published in: (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1109.0975

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