Lie group

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Definition

Let k be a field with an analytic structure on it. A Lie group over k is a group equipped with the structure of an analytic manifold over k, such that the group multiplication and the inverse map preserve the analytic structure.

The field k is typically the field of real numbers, field of complex numbers, or some field extension of the p-adics. See below for the various more specific notions of Lie group: