A Projective Representations of the Thompson Group F and Its Lifting Problem

Jun Yang

Published 2018-12-04Version 1

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 know this projective unitary representation may cannot be lifted to a unitary one. We will mainly discuss the lifting problem of this projective representation.