Abstract
Many Lie algebras occur naturally as subalgebras of the Lie algebras of linear transformations of vector spaces. Even more are easily seen to be isomorphic to such subalgebras. Given such a Lie algebra, one can profitably use linear algebra to study its properties.
Throughout this chapter, we let V denote an n-dimensional vector space over a field F. We consider some elementary facts concerning linear maps and Lie subalgebras of gl(V) which are needed for the theorems to come.
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© 2006 Springer-Verlag London Limited
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Erdmann, K., Wildon, M.J. (2006). Subalgebras of gl(V). In: Introduction to Lie Algebras. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/1-84628-490-2_5
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DOI: https://doi.org/10.1007/1-84628-490-2_5
Publisher Name: Springer, London
Print ISBN: 978-1-84628-040-5
Online ISBN: 978-1-84628-490-8
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