Abstract
The semi-simple algebras and their representations play a central role in applications to physical examples. For example, so(3), su(2), so(3, 1) and su(3) are all (real) semi-simple algebras. The complex semi-simple algebras were originally classified by Killing and Cartan in his thesis (1894); and later (1914) Cartan classified the real ones. We discuss these matters in some detail in this chapter; but before launching into an abstract algebraic development, we ease into the subject with two simple examples.
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© 1986 Springer-Verlag Berlin Heidelberg
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Sattinger, D.H., Weaver, O.L. (1986). Structure of Semi-Simple 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_10
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DOI: https://doi.org/10.1007/978-1-4757-1910-9_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3077-4
Online ISBN: 978-1-4757-1910-9
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