even locally homeomorphism example diff '''s''' sup sup one may find diffeomorphisms arbitrarily close identity image exp furthermore infinite dimensional lie algebras lie algebra group real form complexification given complex lie algebra math mathfrak g math real lie algebra math mathfrak g math said ' 'real form'' math mathfrak g math complexification math mathfrak g otimes mathbb r mathbb c simeq mathfrak g math isomorphic math mathfrak g math ref name fulton ref real form need unique example math mathfrak sl mathbb c math two real forms math mathfrak sl mathbb r math
Formal science Mathematics Pure mathematics Algebra Lie algebra