Pacific Ocean Asia) is in the Eastern Hemisphere, while the "East Pacific" (or "eastern Pacific", near the Americas) is in the Western Hemisphere. The Southern Pacific Ocean harbors the Southeast Indian Ridge crossing from south of Australia turning into the Pacific-Antarctic Ridge (north of the South Pole) and merges with another ridge (south of South America) to form the East Pacific Rise which also connects with another ridge (south of North America) which overlooks the Juan de Fuca Ridge. For most of Magellan's voyage from the Strait of Magellan to the Philippines, the explorer indeed found the ocean peaceful. However, the Pacific
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