ON THE PROJECTIVE SCHUR GROUP OF A FIELD

[摘要] 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 k(alpha)G with G finite, alpha is an element of H-2(G, k*). It has been conjectured by Nelis and Van Oystaeyen (J. Algebra 137 (1991), 501-518) that PS(k) = Br(k) for all fields k. We disprove this conjecture by showing that PS(k) not equal Br(k) for rational function fields k(0)(x) where k(0) is any infinite field which is finitely generated over its prime field. (C) 1995 Academic Press. Inc.

[发布日期] 1995-12-01