A projective unitary representation of a group 
is a map 
into the unitary operators on a complex Hilbert space for which
 |
where 
is a scalar 2-cocycle. For normalized data, 
and 
.
Associativity requires 
.
An ordinary unitary representation is the
case 
. A cocycle is of finite
type if it admits such a representation with nonzero finite-dimensional
. Finite type does not require
the image of the representation to be finite.
-Superrigidity for Cocycle Twisted Group von Neumann Algebras."
Invent. Math. 240, 193-260, 2025.