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 group–Lie algebra correspondence Lie group–Lie algebra correspondence In mathematics, Lie group–Lie algebra correspondence allows one to study Lie groups, which are geometric objects, in terms of Lie algebras, which are linear objects. In this article, a Lie group refers to a real Lie group. For the complex and "p"-adic cases, see complex Lie group and "p"-adic Lie group. In this article, manifolds (in particular Lie groups) are assumed to be second countable; in particular, they have at most countably many connected components. There are various ways one can understand the construction of the Lie algebra of a Lie group "G". One approach uses