On the projective schur group of a field

TY - JOUR

T1 - On the projective schur group of a field

AU - Aljadeff, E.

AU - Sonn, J.

PY - 1995/12/1

Y1 - 1995/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0000040784&partnerID=8YFLogxK

U2 - 10.1006/jabr.1995.1364

DO - 10.1006/jabr.1995.1364

M3 - 文章

AN - SCOPUS:0000040784

SN - 0021-8693

VL - 178

SP - 530

EP - 540

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -