Air transportation in the Philippines Air transportation in the Philippines Air transportation in the Philippines goes back to the early days of aviation prior to World War II, during the American colonial period of the Philippines. Currently, the Philippines has several registered airline companies, but they are mostly chartered. There are two main domestic airline groups doing business as Philippine Airlines and Cebu Pacific, with AirAsia Philippines competing on some international routes. The domestic market is dominated by the Cebu Pacific group which has a 61% market share, followed by the Philippine Airlines group which has 29%, followed by AirAsia, having a 9% share. Prior
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