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 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