Ocean acidification in the Arctic Ocean has also allowed more Pacific water to flow into in the Arctic ocean during the winter, this is called Pacific winter water. The Pacific water flows into the Arctic ocean carrying additional amounts of carbon dioxide by being exposed to the atmosphere and absorbing carbon dioxide from decaying organic matter and from sediments. The Arctic ocean pH levels are rapidly decreasing because not only is the ocean water absorbing more carbon dioxide due to increased surface area exposure as a result of a decrease in sea ice. It also has large amounts of carbon dioxide being transferred to the Arctic
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