Title: On finite degree partial representations of groups
Abstract: 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.