On the generators of semisimple lie algebras |
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Authors: | Tudor Ionescu |
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Affiliation: | Division of Engineering and Applied Physics Harvard University Cambridge, Massachusetts, USA;Department of Electrical Engineering University of Massachusetts Amherst, Massachusetts, USA |
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Abstract: | It will be shown that given any element X in a simple Lie algebra over C, there exists a Y ∈ such that the Lie algebra generated by X and Y is . The result is extended to the real semisimple Lie algebras. In some sense the main theorem of this paper can be regarded as an extension of Morozov-Jacobson theorem concerning three dimensional simple Lie algebras (see the remark at the end of Sec. 4). A new property of a special class of regular elements, known as the cyclic elements, is given. |
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