Projective schur algebras over a field of positive characteristic

Abstract

If the characteristic of a field K is not zero then the Schur group S(K) = 0. In this paper we ask a similar question for the projective Schur group PS(K) and prove that the subgroup of PS(K) consisting of radical algebras is trivial. This disproves the conjecture that every projective Schur algebra is similar to a radical algebra.