Projective Schur Division Algebras Are Abelian Crossed Products Original Research Article

Let k be a field. A projective Schur Algebra over k is a finite-dimensional k-central simple algebra which is a homomorphic image of a twisted group algebra kαG with G a finite group and α set membership, variant H2(G, k*). The main result of this paper is that every projective Schur division algebra is an abelian crossed product (K/k, ƒ), where K is a radical extension of k.