Captaincy General of the Philippines administrative units: Spanish rule in the Philippines ceased in 1898 after the war with the United States, which annexed most territories, although the administrative jurisdictions remained intact. Most of the remaining territories in the Pacific Ocean were sold to Germany during the German-Spanish Treaty of 1899. Captaincy General of the Philippines The Captaincy General of the Philippines ( ; ) was an administrative district of the Spanish Empire in Southeast Asia governed by a Governor-General. The Captaincy General encompassed the Spanish East Indies, which included among others the Philippine Islands and the Caroline Islands. It was founded in 1565 with
Lie theory Lie theory In mathematics, the researcher Sophus Lie ( ) initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory. For instance, the latter subject is Lie sphere geometry. This article addresses his approach to transformation groups, which is one of the areas of mathematics, and was worked out by Wilhelm Killing and Élie Cartan. The foundation of Lie theory is the exponential map relating Lie algebras to Lie groups which is called the Lie group–Lie algebra correspondence. The subject is part of differential geometry since Lie