Topological groups, Lie groups Structure of Lie groups Concept
Solvable Lie group
Summary
A solvable Lie group is a connected Lie group that is a solvable group: its derived series reaches the trivial group after finitely many steps. Equivalently, its Lie algebra is a solvable Lie algebra. Solvable Lie groups are the counterpart of semisimple ones. By the Levi decomposition, every connected Lie group is built from a solvable normal subgroup and a semisimple part. Typical examples are groups of invertible upper triangular matrices.
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About this page
| Tag | 9CNSVFQ801 |
|---|---|
| URI | m2://9CNSVFQ801 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 22E25, 22E15, 20F16 |
| Specializes | Lie group, Solvable group |
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