 Lie group-Lie algebra correspondence

Every Lie algebra corresponds to a single simply connected Lie group.

The Baker-Campbell-Hausdorff formula basically defines how to map an algebra to the group.

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The Lie group–Lie algebra correspondence is a fundamental concept in mathematics that relates Lie groups and Lie algebras, which are both central in the study of continuous symmetries and their structures. Here’s a breakdown of the concepts and their relationship: ### Lie Groups - A **Lie group** is a smooth manifold that also has a group structure such that the group operations (multiplication and inversion) are smooth maps. Lie groups are used to describe continuous symmetries (e.g.