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A fruitful strategy, going back to Sophus Lie (1842–1899), for investigating a Lie group consists of linearizing it at the identity element. The infinitesimal deviations of the group elements from the identity element form the linear tangent space at the identity element—this is the Lie algebra \(\mathfrak {g}\) associated with a Lie group G.

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Lie Algebras of Lie Groups

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  • 发表日期：

    2026年

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  • Andreas Wipf

摘要

A fruitful strategy, going back to Sophus Lie (1842–1899), for investigating a Lie group consists of linearizing it at the identity element. The infinitesimal deviations of the group elements from the identity element form the linear tangent space at the identity element—this is the Lie algebra \(\mathfrak {g}\) associated with a Lie group G.