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
Famous quotes containing the words solvable, lie and/or groups:
“The problems of the world, AIDS, cancer, nuclear war, pollution, are, finally, no more solvable than the problem of a tree which has borne fruit: the apples are overripe and they are falling—what can be done?... Nothing can be done, and nothing needs to be done. Something is being done—the organism is preparing to rest.”
—David Mamet (b. 1947)
“O mighty Caesar! Dost thou lie so low?
Are all thy conquests, glories, triumphs, spoils,
Shrunk to this little measure? Fare thee well.”
—William Shakespeare (1564–1616)
“Trees appeared in groups and singly, revolving coolly and blandly, displaying the latest fashions. The blue dampness of a ravine. A memory of love, disguised as a meadow. Wispy clouds—the greyhounds of heaven.”
—Vladimir Nabokov (1899–1977)