On finite degree partial representations of groups

We establish a one-to-one correspondence between the irreducible finite degree partial representations of a group G and the (usual) irreducible representations of certain ideals of a groupoid algebra constructed from G. We derive a structural result about the irreducible partial representations on finite dimensional vector spaces and give the description “up to usual representations” of the irreducible partial representations of abelian groups of degrees 4. We treat simultaneously irreducible and indecomposable partial representations