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        "quote": "where $X$ is any smooth vector field. On the right-hand side of <a href=\"#equation-19-1\" class=\"cross-reference\" id=\"xref-01-lie-groups-4\" data-reference=\"equation-19-1\">Eq. (19.1)</a> $L _ { g * }$ is the tangent map at the point $g ^ { - 1 } a$ . A vector field $X$ on $G$ is said to be <u class=\"concept-term\" data-concept-identity=\"urn:uuid:5b63b7cd-d37a-4f98-9472-ac67fe1c2dae\" data-concept-route=\"/concept-identities#concept-5b63b7cd-d37a-4f98-9472-ac67fe1c2dae\" id=\"first-861f00be2d1f56c10a36-en\">left-invariant</u> if $L _ { g * } X = X$ for all $g \\in G$",
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