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:
“The others “acted” a role; I was the role. She who was Mary Garden died that it might live. That was my genius ... and my sacrifice. It drained off so much of me that by comparison my private life was empty. I could not give myself completely twice.”
—Mary Garden (1874–1967)
“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)
“His very words are instinct with spirit; each is as a spark, a burning atom of inextinguishable thought; and many yet lie covered in the ashes of their birth and pregnant with a lightning which has yet found no conductor.”
—Percy Bysshe Shelley (1792–1822)