Criteria for quasi-symmetricity and the holomorphic sectional curvature of a homogeneous bounded domain
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)\({}^ t\).
scientific article; zbMATH DE number 4129192
scientific article