As A Universal Enveloping Algebra
The symmetric algebra S(V) is the universal enveloping algebra of an abelian Lie algebra, i.e. one in which the Lie bracket is identically 0.
Read more about this topic: Symmetric Algebra
Famous quotes containing the words universal, enveloping and/or algebra:
“Vanity, or to call it by a gentler name, the desire of admiration and applause, is, perhaps, the most universal principle of human actions.... Where that desire is wanting, we are apt to be indifferent, listless, indolent, and inert.... I will own to you, under the secrecy of confession, that my vanity has very often made me take great pains to make many a woman in love with me, if I could, for whose person I would not have given a pinch of snuff.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“Our religion vulgarly stands on numbers of believers. Whenever the appeal is made—no matter how indirectly—to numbers, proclamation is then and there made, that religion is not. He that finds God a sweet, enveloping presence, who shall dare to come in?”
—Ralph Waldo Emerson (1803–1882)
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)