Partial Representations and Partial Group Algebras

The partial group algebra of a group G over a field K, denoted by Kpar(G), is the algebra whose representations correspond to the partial representations of G over K-vector spaces. In this paper we study the structure of the partial group algebra Kpar(G), where G is a finite group. In particular, given two finite abelian groups G1 and G2, we prove that if the characteristic of K does not divide the order of G1, then Kpar(G1) is isomorphic to Kpar(G2) if and only if G1 is isomorphic to G2.