Abstract
Two decades after his doctoral dissertation, Cartan published a “trilogy” of memoirs [1913; 1914b; 1914c] of fundamental importance to the theory of Lie groups and algebras and especially to the study of their representations. In [1913] he further developed Killing’s theory of secondary roots and applied it to the problem of determining all linear Lie algebras of semisimple structure that leave nothing planar invariant. That is, he solved the representation problem that he had already articulated twenty years earlier in his dissertation. In [1914b] he solved the same problem for real linear Lie algebras. This required the results of [1913] together with the classification of all real simple structures that he developed in [1914c].
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© 2000 Springer Science+Business Media New York
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Hawkins, T. (2000). Cartan’s Trilogy: 1913–14. In: Emergence of the Theory of Lie Groups. Sources and Studies in the History of Mathematics and Physical Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1202-7_8
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DOI: https://doi.org/10.1007/978-1-4612-1202-7_8
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