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Preliminary of Lie Algebras

In: Representations of Lie Algebras and Partial Differential Equations

Author

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  • Xiaoping Xu

    (Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Institute of Mathematics
    University of Chinese Academy of Sciences, School of Mathematics)

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.

Suggested Citation

  • Xiaoping Xu, 2017. "Preliminary of Lie Algebras," Springer Books, in: Representations of Lie Algebras and Partial Differential Equations, chapter 0, pages 3-32, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-6391-6_1
    DOI: 10.1007/978-981-10-6391-6_1
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