Partial representations and partial group algebras

The partial group algebra of a group G over a field K, denoted by K-par(G), is the algebra whose representations correspond to the partial representat ions of G over K-vector spaces. In this paper we study the structure of the partial group algebra K-par(G), where G is a finite group. In particular, given two finite abelian groups G(1) and G(2), we prove that if the charact eristic of ii does not divide the order of G(1), then K-par(G(1)) is isomor phic to K-par(G(2)) if and only if G(1) is isomorphic to G(2). (C) 2000 Aca demic Press.