Partial Representations and Partial Group Algebras

الأصل · EN

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 is zero, then Kpar(G₁) is isomorphic to Kpar(G₂) if and only if G₁ is isomorphic to G₂.