Pacific Ocean width at about 5°N latitude, where it stretches approximately from Indonesia to the coast of Colombia—halfway around the world, and more than five times the diameter of the Moon. The lowest known point on Earth—the Mariana Trench—lies below sea level. Its average depth is , putting the total water volume at roughly . Due to the effects of plate tectonics, the Pacific Ocean is currently shrinking by roughly per year on three sides, roughly averaging a year. By contrast, the Atlantic Ocean is increasing in size. Along the Pacific Ocean's irregular western margins lie many seas, the largest of which
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