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- Summary
- Is the exponential an approximation to the first order?

Is it correct saying that the Exponential limit is an exact solution for passing from a Lie Algebra to a Lie group because a differential manifold with Lie group structure is such that for any point of the transformation the tangent space is by definition the Lie algebra: is that the underlying assumption to write a generalized transformation as that limit?

Or which is the intuition: how is the infinitesimal transformation in the neighborhood of the identity generalized to a finite distance?

Or which is the intuition: how is the infinitesimal transformation in the neighborhood of the identity generalized to a finite distance?