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The Lie algebra of a Lie subgroup, as we saw, is in a natural fashion a Lie subalgebra of the Lie algebra of the ambient group. A central result of Lie theory is a converse of this assertion, due to Lie, and is known as the Fundamental Theorem of Lie Theory. Before proceeding to formulate and prove such a converse, we will establish a Lemma and a theorem due to Cartan, which we will use in the proof of the converse.

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Lie Groups: The Theorems of Cartan and Lie

  • 章节

  • 发表日期：

    2025年

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  • M. S. Raghunathan

摘要

The Lie algebra of a Lie subgroup, as we saw, is in a natural fashion a Lie subalgebra of the Lie algebra of the ambient group. A central result of Lie theory is a converse of this assertion, due to Lie, and is known as the Fundamental Theorem of Lie Theory. Before proceeding to formulate and prove such a converse, we will establish a Lemma and a theorem due to Cartan, which we will use in the proof of the converse.