A Projective Representations of the Thompson Group F and Its Lifting Problem
The Thompson group $F$ has a canonical unitary representation on $H=L^2[0,1]$. With a special projection, we construct a projective unitary representation on a Fermionic Fock space associated with $H$. This comes from the representation of the CAR algebra of $H$. Then, by computing the 2nd cohomology group, we will be able to decide if this projective unitary representation can be lifted to an ordinary representation. We will mainly discuss the lifting problem of this projective representation.