I am struggling to understand how to find the form of the exponential map of the lie algebra of a lie group. That is: given a Lie group $G$ such that $T_1G$ is it's Lie algebra (which is isomorphic to the space of left invariant vector fields) how do we define the exponential $$e^{tX}, \quad X \in T_1G$$ I know for linear groups this exponential map is just the matrix exponential. However for a general Lie group this is unclear.
2026-04-04 05:21:02.1775280062
Defining the exponential of a Lie algebra of a Lie group.
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