The present paper investigates a natural generalization of the duality between Riemannian symmetric pairs of compact type and those of non-compact type à la É. Cartan. The main result of this paper is to construct an explicit description of a one-to-one correspondence between non-compact pseudo-Riemannian semisimple symmetric pairs and commutative compact semisimple symmetric triads, which is called the duality theorem. Further, we develop a general theory of the duality theorem.

中文翻译：

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非紧致半对称对称对与交换紧致半对称对称三元对偶及其一般理论

本文研究了紧凑型黎曼对称对和非紧凑型黎曼对称对之间的对偶性的自然概括。卡丹。本文的主要结果是构造一个非紧致伪黎曼半简单对称对与交换紧致半简单对称三合一之间一一对应关系的显式描述，称为对偶定理。此外，我们发展了对偶定理的一般理论。