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 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