Editing Projective linear group (section)

== Representation theory ==
{{main|Projective representation}}
[[File:Projective-representation-lifting.svg|225px|thumb|A [[projective representation]] of ''G'' can be pulled back to a [[linear representation]] of a [[central extension (mathematics)|central extension]] ''C'' of ''G''. ''K''<sup>*</sup> = ''K''<sup>×</sup>.]]
A [[group homomorphism]] {{nowrap|''G'' → PGL(''V'')}} from a group ''G'' to a projective linear group is called a [[projective representation]] of the group ''G'', by analogy with a [[linear representation]] (a homomorphism {{nowrap|G → GL(''V'')}}). These were studied by [[Issai Schur]], who showed that ''projective'' representations of ''G'' can be classified in terms of ''linear'' representations of [[central extension (mathematics)|central extensions]] of ''G''. This led to the [[Schur multiplier]], which is used to address this question.