Reductive Lie Algebra
In mathematics, a Lie algebra is reductive if its adjoint representation is completely reducible, whence the name. More concretely, a Lie algebra is reductive if is a direct sum of a semisimple Lie algebra and an abelian Lie algebra: there are alternative characterizations, given below.
Read more about Reductive Lie Algebra: Examples, Definitions, Properties
Famous quotes containing the words reductive, lie and/or algebra:
“In the haunted house no quarter is given: in that respect
It’s very much business as usual. The reductive principle
Is no longer there, or isn’t enforced as much as before.”
—John Ashbery (b. 1927)
“Romeo. I dreamt a dream tonight.
Mercutio. And so did I.
Romeo. Well, what was yours?
Mercutio. That dreamers often lie.
Romeo. In bed asleep, while they do dream things true.
Mercutio. O then I see Queen Mab hath been with you.
She is the fairies’ midwife, and she comes
In shape no bigger than an agate stone
On the forefinger of an alderman,
Drawn with a team of little atomi
Over men’s noses as they lie asleep.”
—William Shakespeare (1564–1616)
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)