Every projective Schur algebra is Brauer equivalent to a radical abelian algebra

Details Every projective Schur algebra is Brauer equivalent to a radical abelian algebra Every projective Schur algebra is Brauer equivalent to a radical abelian algebra

2006-07-04

arxiv.org/abs/math/0607087v1

Mathematics

Representation Theory

10 pages

Scientific paper

We prove that any projective Schur algebra over a field $K$ is equivalent in $Br(K)$ to a radical abelian algebra. This was conjectured in 1995 by Sonn and the first author of this paper. As a consequence we obtain a characterization of the projective Schur group by means of Galois cohomology. The conjecture was known for algebras over fields of positive characteristic. In characteristic zero the conjecture was known for algebras over fields with an Henselian valuation over a local or global field of characteristic zero.

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