Parabolic Lie algebra
（重定向自Parabolic subalgebra）
In algebra, a parabolic Lie algebra ![\mathfrak p](/Images/godic/202502/01/bd21fa57c2328f31b1fa48272803bfc40351.png")
is a subalgebra of a semisimple Lie algebra ![\mathfrak g](/Images/godic/202502/01/999cf6f64760406a9147451281d591ad0352.png")
satisfying one of the following two conditions:
These conditions are equivalent over an algebraically closed field of characteristic zero, such as the complex numbers. If the field ![\mathbb F](/Images/godic/202502/01/d8425fd4b87ab4a0b3c37db8afaa3d340352.png")
is not algebraically closed, then the first condition is replaced by the assumption that