On the rational structures of symmetric domains. II: Determination of rational points of classical domains
type: Item
instance of: scholarly article
title: On the rational structures of symmetric domains. II: Determination of rational points of classical domains
zbMATH Open document ID: 0813.32029
author: Ichirō Satake
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1992-08-13T00:00:00Z
review text: In Part I [International Symposium in Memory of Hua Loo Keng, Vol. II (Beijing, 1988) Springer, Berlin, 231-259 (1991; see the paper above)] the author gave an algebraic formulation of the Siegel domain realization of symmetric spaces and applied it to the determination of rational points. In the present paper, a list of pure \(\mathbb{Q}\)-simple classical Lie algebras of Hermitian type is given. A method of determining rational points of a domain is explained. The main theorems give necessary and sufficient conditions for the existence of rational points with a given CM-field according to the respective types rational points.
Mathematics Subject Classification ID: 32M15
Mathematics Subject Classification ID: 32N10
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 40909
zbMATH Keywords: symmetric domains
zbMATH Keywords: rational points
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227462
OpenAlex ID: W2034618169
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DOI: 10.2748/TMJ/1178227462
description: scientific article; zbMATH DE number 40909