Abstract
In this lecture we introduce the definitions and basic examples of Lie groups and Lie algebras. We assume here familiarity with the definition of differentiable manifolds and maps between them, but no more; in particular, we do not mention vector fields, differential forms, Riemannian metrics, or any other tensors. Section 7.3, which discusses maps of Lie groups that are covering space maps of the underlying manifolds, may be skimmed and referred back to as needed, though working through it will help promote familiarity with basic examples of Lie groups.
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© 2004 Springer Science+Business Media New York
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Fulton, W., Harris, J. (2004). Lie Groups. In: Representation Theory. Graduate Texts in Mathematics, vol 129. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0979-9_7
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DOI: https://doi.org/10.1007/978-1-4612-0979-9_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-3-540-00539-1
Online ISBN: 978-1-4612-0979-9
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