Projective Schur Division Algebras Are Abelian Crossed Products

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 k α G with G a finite group and α ∈ H 2( 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.