I am studying lie algebra myself and question is about finding dimension of lie algebra . While i read Wikipedia link about lie algebra and lie group i saw statement
Lie algebra $\mathfrak{g}$ is finite-dimensional and it has the same dimension as the manifold $G$
How can i proof this statement actually i have no idea Please firstly give me a hint.
Another point of view is that you can consider Lie algebras independently of manifolds. Then a Lie algebra $L$ is just a vector space $V$ with a bilinear product, which is skew-symmetric and satisfies the Jacobi identity. Then $\dim L=\dim V$ is the dimension as a vector space. For example, the Heisenberg Lie algebra $L$ with basis $x,y,z$ and $[x,y]=z$ is $3$-dimensional.