Real forms of a Lie algebra
imported>Pythagoras0님의 2012년 9월 17일 (월) 22:11 판 (새 문서: ==introduction== * a complex Lie algbera L can be regarded as a real Lie algebra <math>L^{R}</math> * if <math>L^{R}=L_0\oplus i L_0</math> for some real subalgebra <math>L_0</math> *...)
introduction
- a complex Lie algbera L can be regarded as a real Lie algebra \(L^{R}\)
- if \(L^{R}=L_0\oplus i L_0\) for some real subalgebra \(L_0\)
- \(L_0\) is called a real from of \(L\)
- split real forms
- compact real forms
compact real forms
- of all the real forms of a given simple complex Lie algebra, there is precisely one which is the real Lie algebra of a compact Lie group
- a real Lie algebra which is the Lie algebra of some compact group is called compact