Solvable Lie Groups
The terminology arises from the solvable groups of abstract group theory. There are several possible definitions of solvable Lie group. For a Lie group G, there is
- termination of the usual derived series, in other words taking G as an abstract group;
- termination of the closures of the derived series;
- having a solvable Lie algebra.
To have equivalence one needs to assume G connected. For connected Lie groups, these definitions are the same, and the derived series of Lie algebras are the Lie algebra of the derived series of (closed) subgroups.
Read more about this topic: Solvable Lie Algebra
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