Abstract
We give basic concepts and examples of Lie algebras. Moreover, Engel’s theorem on nilpotent Lie algebras and Lie’s theorem on solvable Lie algebras are proved. Furthermore, we derive the Jordan-Chevalley decomposition of a linear transformation and use it to show Cartan’s criterion on the solvability.
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Xu, X. (2017). Preliminary of Lie Algebras. In: Representations of Lie Algebras and Partial Differential Equations. Springer, Singapore. https://doi.org/10.1007/978-981-10-6391-6_1
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DOI: https://doi.org/10.1007/978-981-10-6391-6_1
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Online ISBN: 978-981-10-6391-6
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