input: How is the Lie algebra of a Lie group defined and what is its relationship to the group?

answers: The Lie algebra of a Lie group G, denoted Lie(G), is the set of all X in Mat_n(ℂ) such that exp(tX) ⊂ G for all t. It is a vector space whose dimension is equal to the dimension of G as a manifold, and it is a Lie subalgebra of gl(n, ℂ).

label: mathematics

title: Lie Groups