On the projective schur group of a field

E. Aljadeff, J. Sonn

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Abstract

If k is a field, the projective Schur group PS(k) of k is the subgroup of the Brauer group Br(k) consisting of those classes which contain a projective Schur algebra, i.e., a homomorphic image of a twisted group algebra kαG with G finite, α ∈ H2(G, k*). It has been conjectured by Nelis and Van Oystaeyen (J. Algebra137 (1991), 501-518) that PS(k) = Br(k) for all fields k. We disprove this conjecture by showing that PS(k) ≠ Br(k) for rational function fields k0(x) where k0 is any infinite field which is finitely generated over its prime field.

Original languageEnglish
Pages (from-to)530-540
Number of pages11
JournalJournal of Algebra
Volume178
Issue number2
DOIs
StatePublished - 1 Dec 1995
Externally publishedYes

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