Abstract
We have said that a Lie group is an analytic manifold; and so it makes sense to talk about the tangent space to that manifold, and in particular the tangent space at the identity of the group. That tangent space is called the Lie algebra. In the case of a linear group it can be computed explicitly by differentiating curves through the identity.
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© 1986 Springer-Verlag Berlin Heidelberg
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Sattinger, D.H., Weaver, O.L. (1986). Lie Algebras. In: Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics. Applied Mathematical Sciences, vol 61. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1910-9_2
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DOI: https://doi.org/10.1007/978-1-4757-1910-9_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3077-4
Online ISBN: 978-1-4757-1910-9
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