Solvable Lie Algebra
In mathematics, a Lie algebra g is solvable if its derived series terminates in the zero subalgebra. That is, writing
for the derived Lie algebra of g, generated by the set of values
for x and y in g, the derived series
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.
A maximal solvable subalgebra is called a Borel subalgebra. The largest solvable ideal is called the radical.
Read more about Solvable Lie Algebra: Properties, Completely Solvable Lie Algebras, Example, Solvable Lie Groups
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