Solvable Lie Algebra
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High Quality Content by WIKIPEDIA articles! In mathematics, a Lie algebra g is solvable if its derived series terminates in the zero subalgebra. That is, writing [mathfrak{g},mathfrak{g}] for the derived Lie algebra of g, generated by the [x,y] for x and y in g, the derived series mathfrak{g} geq [mathfrak{g},mathfrak{g}] geq [[mathfrak{g},mathfrak{g}],[mathfrak{g},mathfrak{g}]] geq [[[mathfrak{g},mathfrak{g}],[mathfrak{g},mathfrak{g}]],[[mathfrak{g},mathfrak{g}],[mathfrak{g},mathfrak{g}]]] geq ... becomes constant eventually at 0. Any nilpotent Lie algebra is solvable, a fortiori, but the converse is not true. The solvable Lie algebras and the semisimple Lie algebras form two large and generally complementary classes, as is shown by the Levi decomposition.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131355585
- Editor Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
- Genre Mathematik
- EAN 9786131355585
- Titel Solvable Lie Algebra
- Herausgeber Betascript Publishing
- Anzahl Seiten 72
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