Basis
A basis for the Witt algebra is given by the vector fields, for n in .
The Lie bracket of two vector fields is given by
This algebra has a central extension called the Virasoro algebra that is important in conformal field theory and string theory.
Read more about this topic: Witt Algebra
Famous quotes containing the word basis:
“That food has always been, and will continue to be, the basis for one of our greater snobbisms does not explain the fact that the attitude toward the food choice of others is becoming more and more heatedly exclusive until it may well turn into one of those forms of bigotry against which gallant little committees are constantly planning campaigns in the cause of justice and decency.”
—Cornelia Otis Skinner (1901–1979)
“The self ... might be regarded as a sort of citadel of the mind, fortified without and containing selected treasures within, while love is an undivided share in the rest of the universe. In a healthy mind each contributes to the growth of the other: what we love intensely or for a long time we are likely to bring within the citadel, and to assert as part of ourself. On the other hand, it is only on the basis of a substantial self that a person is capable of progressive sympathy or love.”
—Charles Horton Cooley (1864–1929)
“Protoplasm, simple or nucleated, is the formal basis of all life. It is the clay of the potter: which, bake it and paint it as he will, remains clay, separated by artifice, and not by nature from the commonest brick or sun-dried clod.”
—Thomas Henry Huxley (1825–1895)