Criteria for quasi-symmetricity and the holomorphic sectional curvature of a homogeneous bounded domain
type: Item
instance of: scholarly article
title: Criteria for quasi-symmetricity and the holomorphic sectional curvature of a homogeneous bounded domain
zbMATH Open document ID: 0689.32013
author: Kazuo Azukawa
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1989-01-01T00:00:00Z
review text: The interest of the normal j-algebras comes from the fact that there is a bijective correspondence between them and bounded homogeneous domains in some \({\mathbb{C}}^ n\). For such an algebra \({\mathcal J}\), Piatetski-Shapiro has given a root \({\mathcal J}=\Sigma n_{ab}+\Sigma jn_{ab}+\Sigma n_{a\infty}\) (j gives te complex structure). Let be \({\mathcal L}=\Sigma n_{ab}\). There is a natural operation!on \({\mathcal L}\). The case when \({\mathcal L}\) is a Jordan algebra (Property (J)) was studied by Satake because associated domains, called quasi-symmetric domains, have nice properties. In his paper, the author gives equivalent conditions to properties (J). For his proofs, he uses only the algebraic properties of \({\mathcal J}\). Partial results in this direction were given by d'Atri and Miaello and Dorfmeister, using geometry. The author uses the notion of a strong ideal of \({\mathcal J}\), which is an ideal inariant by (ad x)\({}^ t\).
reviewed by: Jean-Jacques Loeb
Mathematics Subject Classification ID: 32M10
Mathematics Subject Classification ID: 32M15
Mathematics Subject Classification ID: 17C10
zbMATH DE Number: 4129192
zbMATH Keywords: normal j-algebra
zbMATH Keywords: bounded homogeneous domains
zbMATH Keywords: Jordan algebra
zbMATH Keywords: quasi- symmetric domains
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227775
OpenAlex ID: W2011618949
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DOI: 10.2748/TMJ/1178227775
description: scientific article; zbMATH DE number 4129192