Abstract
Abelian Lie algebras are easily understood. There is a sense in which some of the low-dimensional Lie algebras we studied in Chapter 3 are close to being abelian. For example, the 3-dimensional Heisenberg algebra discussed in §3.2.1 has a 1-dimensional centre. The quotient algebra modulo this ideal is also abelian. We ask when something similar might hold more generally. That is, to what extent can we “approximate” a Lie algebra by abelian Lie algebras?
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© 2006 Springer-Verlag London Limited
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Erdmann, K., Wildon, M.J. (2006). Solvable Lie Algebras and a Rough Classification. In: Introduction to Lie Algebras. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/1-84628-490-2_4
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DOI: https://doi.org/10.1007/1-84628-490-2_4
Publisher Name: Springer, London
Print ISBN: 978-1-84628-040-5
Online ISBN: 978-1-84628-490-8
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