Tsukuba Journal of Mathematics

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

Akihiro Nishio

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Abstract

Let J1 be the real form of a complex simple Jordan algebra such that the automorphism group is F4(−20). By using some orbit types of F4(−20) on J1, for F4(−20), explicitly, we give the Iwasawa decomposition, the Oshima-Sekiguchi's Kε-Iwasawa decomposition, the Matsuki decomposition, and the Bruhat and Gauss decompositions.

Article information

Source
Tsukuba J. Math., Volume 37, Number 1 (2013), 85-119.

Dates
First available in Project Euclid: 15 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1373893407

Digital Object Identifier
doi:10.21099/tkbjm/1373893407

Mathematical Reviews number (MathSciNet)
MR3112420

Zentralblatt MATH identifier
1364.17029

Subjects
Primary: 20G41: Exceptional groups
Secondary: 17C30: Associated groups, automorphisms 57S20: Noncompact Lie groups of transformations

Citation

Nishio, Akihiro. The Iwasawa decomposition and the Bruhat decomposition of the automorphism group on certain exceptional Jordan algebra. Tsukuba J. Math. 37 (2013), no. 1, 85--119. doi:10.21099/tkbjm/1373893407. https://projecteuclid.org/euclid.tkbjm/1373893407


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