Abstract
Nilpotent and semisimple Lie algebras were introduced by W. Killing in 1888. Solvable (or integrable) algebras were introduced earlier by Lie in connection with his research on (algebraic) differential equations. Lie wanted to establish a theory for continuous transformation groups (of the space Rn) which would be analogous to the Galois theory (and in the latter theory the decisive role is played by finite solvable groups.)
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© 1997 Springer Science+Business Media Dordrecht
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Maurin, K. (1997). Nilpotent, Semimple, and Solvable Lie Algebras. In: The Riemann Legacy. Mathematics and Its Applications, vol 417. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8939-0_18
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DOI: https://doi.org/10.1007/978-94-015-8939-0_18
Publisher Name: Springer, Dordrecht
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