Geology of the Pacific Ocean Guinea, and New Zealand lie outside the andesite line. Outside of the andesite line, volcanism is explosive; the Pacific Ring of Fire is the world's foremost belt of explosive volcanism. The Ring of Fire is named after the several hundred active volcanoes that sit above the various subduction zones. In 2009, the deepest undersea eruption ever recorded occurred at the West Mata submarine volcano, a mile beneath the ocean, close to the Tonga-Kermadec Trench, within the Ring of Fire; it was filmed by the US Jason robotic submersible which descended over . The Pacific Ocean is the only ocean which
Lie group Lie groups are called "isomorphic" if there exists a bijective homomorphism between them whose inverse is also a Lie group homomorphism. Equivalently, it is a diffeomorphism which is also a group homomorphism. Isomorphic Lie groups necessarily have isomorphic Lie algebras; it is then reasonable to ask how isomorphism classes of Lie groups relate to isomorphism classes of Lie algebras. The first result in this direction is Lie's third theorem, which states that every finite-dimensional, real Lie algebra is the Lie algebra of some (linear) Lie group. One way to prove Lie's third theorem is to use Ado's theorem, which says