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Lie Groups, Lie Algebras, and Representations pp 49–76Cite as

Lie Algebras

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Part of the book series: Graduate Texts in Mathematics ((GTM,volume 222))

  • A previous version of this book was inadvertently published without the middle initial of the author’s name as “Brian Hall”. For this reason an erratum has been published, correcting the mistake in the previous version and showing the correct name as Brian C. Hall (see DOI http://dx.doi.org/10.1007/978-3-319-13467-3_14). The version readers currently see is the corrected version. The Publisher would like to apologize for the earlier mistake.

Abstract

We now introduce the “abstract” notion of a Lie algebra. In Sect. 3.3, we will associate to each matrix Lie group a Lie algebra. It is customary to use lowercase Gothic (Fraktur) characters such as \(\mathfrak{g}\) and \(\mathfrak{h}\) to refer to Lie algebras.

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Authors and Affiliations

  1. Department of Mathematics, University of Notre Dame, Notre Dame, IN, USA

    Brian Hall

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  1. Brian Hall
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Hall, B. (2015). Lie Algebras. In: Lie Groups, Lie Algebras, and Representations. Graduate Texts in Mathematics, vol 222. Springer, Cham. https://doi.org/10.1007/978-3-319-13467-3_3

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