Completely Solvable Lie Algebras
A Lie algebra g is called completely solvable if it has a finite chain of ideals from 0 to g such that each has codimension 1 in the next. A finite-dimensional nilpotent Lie algebra is completely solvable, and a completely solvable Lie algebra is solvable. Over an algebraically closed field and solvable Lie algebra is completely solvable, but the 3-dimensional real Lie algebra of the group of Euclidean isometries of the plane is solvable but not completely solvable.
Read more about this topic: Solvable Lie Algebra
Famous quotes containing the words completely, solvable and/or lie:
“To be completely woman you need a master, and in him a compass for your life. You need a man you can look up to and respect. If you dethrone him it’s no wonder that you are discontented, and discontented women are not loved for long.”
—Marlene Dietrich (1904–1992)
“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)
“The lakes are something which you are unprepared for; they lie up so high, exposed to the light, and the forest is diminished to a fine fringe on their edges, with here and there a blue mountain, like amethyst jewels set around some jewel of the first water,—so anterior, so superior, to all the changes that are to take place on their shores, even now civil and refined, and fair as they can ever be.”
—Henry David Thoreau (1817–1862)