On the rational structures of symmetric domains. II: Determination of rational points of classical domains (Q1188486)

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.