In mathematics, the complex Witt algebra, named after Ernst Witt, is the Lie algebra of meromorphic vector fields defined on the Riemann sphere that are holomorphic except at two fixed points.
A basis for the Witt algebra is given by the vector fields
The Lie bracket of two basis vector fields is given by This algebra has a central extension called the Virasoro algebra that is important in two-dimensional conformal field theory and string theory.
Taken over the field of complex numbers, this is just the Lie algebra
Conversely, su(1,1) suffices to reconstruct the original algebra in a presentation.