The Virasoro algebras $Vir_c$ are a family of infinite dimensional Lie *-algebras parametrized by a real number $c$, called the central charge.¹
I hear that there exist two critical values of the central charge $c$, where qualitative changes happen to the structure of $Vir_c$ and of its representations. Those are $c=1$, and $c=25$.
I understand what happens at $c=1$. For $c<1$, the invariant sesquilinear form on the Verma modules is not positive definite, and is positive semi-definite for a discrete set of parameters, while for $c\ge 1$, the sesquilinear form is always positive definite (if a certain parameter called $h$ is $\ge 0$).
Can someone explain what happens at $c=25$?
Edit: José Figueroa-O'Farrill's comments have been quite illuminating. I would still like to know if here is a property (such as unitarity) of $Vir_c$ that distinguishes the cases $c<25$, $c=25$, and $c>25$.
¹ Strictly speaking, $Vir_c$ is not a Lie algebra, but only an associative algbera as I want to impose the relation that identifies the central element with 1, and there is no notion of unit in a Lie algebra (see Ben Webster's comment for a better explanation).