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.
Commutation theorem
A Hilbert algebra is an algebra formula_23 with involution "x"→"x"* and an inner product (,) such that
Let "H" be the Hilbert space completion of formula_23 with respect to the inner product and let "J" denote the extension of the involution to a conjugate-linear involution of "H". Define a representation λ and an anti-representation ρ of 
formula_23 on itself by left and right multiplication: