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

DOI10.1112/BLMS/BDM056zbMath1147.16021arXivmath/0607087OpenAlexW2145839022MaRDI QIDQ5427811

Eli Aljadeff, Ángel Del Río

Publication date: 27 November 2007

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/math/0607087

zbMATH Keywords

Brauer groupstwisted group algebrasradical algebrassupersolvable groupsprojective Schur algebrasprojective representationsprojective Schur groupsradical Abelian algebrasradical field extensions

Mathematics Subject Classification ID

Projective representations and multipliers (20C25) Brauer groups (algebraic aspects) (16K50)

Related Items (4)

Every central simple algebra is Brauer equivalent to a Hopf Schur algebra. ⋮ The Schur group of an Abelian number field. ⋮ Projective schur division algebras ⋮ Yetter–Drinfel’d modules over weak Hopf quasigroups

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