Adjoint and Conjugation Actions

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 4 in Lie Groups and Geometric Aspects of Isometric Actions, 2015, pp 85-107 from Springer

Abstract: Abstract Two actions play a central role in the theory of compact Lie groups G: the G-action on itself by conjugation and the adjoint action of G on its Lie algebra 𝔤 $$\mathfrak{g}$$ , which is the linearization of the latter (see Definition 1.36 and Exercise 3.7). The goal of this chapter is to describe classical results on such actions from a geometric viewpoint.

Keywords: Symmetric Space; Maximal Torus; Dynkin Diagram; Polar Action; Adjoint Action (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_4

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DOI: 10.1007/978-3-319-16613-1_4

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