Conformal field theory
The Hilbert space of physical states is a unitary module of the Virasoro algebra corresponding to a fixed value of "c". Stability requires that the energy spectrum of the Hamiltonian be nonnegative. The modules of interest are the highest weight modules of the Virasoro algebra.
Liouville space
In mathematics, a Liouville space, also known as a line space or an extended Hilbert space is Cartesian product of two Hilbert spaces.