Abstract
In this chapter we show how to ‘linearise’ a matrix group G by considering its tangent space at the identity, which has the algebraic structure of a Lie algebra; the definition and basic properties of Lie algebra are introduced in Section 3.1. Amazingly, the Lie algebra of G captures enough of the properties of G to act as a more manageable substitute for many purposes, at least when G is simply connected. The geometric aspects of this will be studied in Chapter 7 when we investigate G as a Lie group.
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© 2002 Springer-Verlag London
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Baker, A. (2002). Tangent Spaces and Lie Algebras. In: Matrix Groups. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-0183-3_3
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DOI: https://doi.org/10.1007/978-1-4471-0183-3_3
Publisher Name: Springer, London
Print ISBN: 978-1-85233-470-3
Online ISBN: 978-1-4471-0183-3
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