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        "quote": "我们称微分形式 $\\alpha$ 是 <u id=\"concept-19-left-invariant-differential-form\" class=\"concept-term\" data-concept-identity=\"urn:uuid:0d343b9b-e689-498e-ae9b-3760b06ca3c1\" data-concept-route=\"/concept-identities#concept-0d343b9b-e689-498e-ae9b-3760b06ca3c1\">左不变微分形式(left-invariant differential form)</u>，如果对所有的 $g \\in G$ 都有 $L _ { g } ^ { * } \\alpha = \\alpha$。它的外微分 $d \\alpha$ 也是左不变的，因为 $L _ { g } ^ { * } \\mathrm { d } \\alpha = \\mathrm { d } L _ { g } ^ { * } \\alpha = \\mathrm { d } \\alpha$。如果 $\\omega$ 是左不变 1-形式，而 $X$ 是左不变向量场，那么 $\\langle \\omega , X \\rangle$ 在 $G _ { : }$ 上是常数，因为",
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