Abstract
In this chapter, the subgroups of a Lie group are studied from the viewpoint of differential calculus. This means that the subgroups considered are Lie groups with a differentiable submanifold structure. The Lie algebra of a Lie subgroup is a subalgebra of the Lie algebra of the ambient group (a subspace of the tangent space at the identity). One of the objectives is to establish the bijection between Lie subalgebras and Lie subgroups; this is done with the help of theorems on the integrability of distributions. (An overview of the theory of integrability of distributions is found in Appendix B, as well as several concepts and results about submanifolds used in this chapter.)
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References
SAN MARTIN, L. A. B. Álgebras de Lie. 2. ed. Editora da Unicamp, 2010.
VARADARAJAN, V. S. Lie groups, Lie algebras and their representations. Prentice-Hall Inc., 1974.
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San Martin, L.A.B. (2021). Lie Subgroups. In: Lie Groups. Latin American Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-61824-7_6
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DOI: https://doi.org/10.1007/978-3-030-61824-7_6
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