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 simply denoted by formula_77.) The homomorphisms theorem (mentioned above as part of the Lie group-Lie algebra correspondence) then says that if formula_78 is the simply connected Lie group whose Lie algebra is formula_56, "every" representation of formula_56 comes from a representation of "G". The assumption that "G" be simply connected is essential. Consider, for example, the rotation group SO(3), which is not simply connected. There is one irreducible representation of the Lie algebra in each dimension, but only the odd-dimensional representations of the Lie algebra come from representations of the group. (This observation is related to the distinction between integer