Basic Results on Lie Groups

Marcos M. Alexandrino and Renato G. Bettiol
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Marcos M. Alexandrino: Instituto de Matemática e Estatística Universidade de São Paulo, Departamento de Matemática
Renato G. Bettiol: University of Pennsylvania, Department of Mathematics

Chapter Chapter 1 in Lie Groups and Geometric Aspects of Isometric Actions, 2015, pp 3-25 from Springer

Abstract: Abstract This chapter gives an introduction to Lie group theory, presenting the main concepts and giving detailed proofs of basic results. Some knowledge of group theory, linear algebra and advanced calculus is assumed. However, as a service to the reader, a few facts about differentiable manifolds are recalled in Appendix A, which can be used as preliminary reading. The following references, which inspire our approach to the subject, can be used for further reading material on the contents of this chapter: Bump [58], Duistermaat and Kolk [79], Fegan [85], Gilmore [97], Gorbatsevich et al. [88, 98–100], Helgason [126], Hilgert and Neeb [128], Hsiang [129], Knapp [145], Onishchik [179], Spivak [198], Varadarajan [216] and Warner [227].

Keywords: Adjoint Representation; Embed Submanifold; Advanced Calculus; Preliminary Reading; Constant Rank Theorem (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-16613-1_1

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DOI: 10.1007/978-3-319-16613-1_1

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