Last Updated：2025/11/22

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(topology) Any group that is a smooth manifold and whose group operations are differentiable.

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Lie group

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Source Word

Lie group

Noun

(topology) Any group that is a smooth manifold and whose group operations are differentiable.

Japanese Meaning

滑らかな多様体の構造を持ち、その群演算（乗法および逆元の操作）が微分可能である群。

What is this buttons?

A Lie group often serves as the mathematical model for continuous symmetries in physics.

Google Translation / DeepL Translation

群演算が微分可能な滑らかな多様体である群は、物理学における連続対称性の数学的モデルとしてしばしば用いられる。

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Sense（1）

(topology) Any group that is a smooth manifold and whose group operations are differentiable.

Every connected Lie group is homotopically equivalent to its maximal compact subgroup. This reduces the study of the homotopy and homology of Lie groups to the compact case.

Google Translation / DeepL Translation

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Lie groups

（ plural ）

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Lie group

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Lie group

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