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In this chapter we make the connection between Lie groups and Lie algebras. We begin by explaining how to produce a Lie algebra from a Lie group. The converse—producing a Lie group from a Lie algebra—is harder. This is the content of the famous Lie Correspondence Theorem, stated as Theorem 11.11 below. The proof of the Lie Correspondence Theorem will be given in Chapter 14 .

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The Lie Algebra of a Lie Group

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  • 发表日期：

    2026年

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  • Will J. Merry

摘要

In this chapter we make the connection between Lie groups and Lie algebras. We begin by explaining how to produce a Lie algebra from a Lie group. The converse—producing a Lie group from a Lie algebra—is harder. This is the content of the famous Lie Correspondence Theorem, stated as Theorem 11.11 below. The proof of the Lie Correspondence Theorem will be given in Chapter 14 .