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

TY - JOUR

T1 - Every projective Schur algebra is Brauer equivalent to a radical abelian algebra

AU - Aljadeff, Eli

AU - Del Río, Ángel

N1 - Funding Information: This research was carried while the first author was visiting the University of Murcia during the spring semester of 2005/6. He thanks the Department of Mathematics for the hospitality and Fundación Séneca of Murcia for their financial support. The second author has been partially supported by D.G.I. of Spain and Fundación Séneca of Murcia.

PY - 2007/10

Y1 - 2007/10

N2 - 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 a Henselian valuation over a local or global field of characteristic zero.

AB - 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 a Henselian valuation over a local or global field of characteristic zero.

UR - http://www.scopus.com/inward/record.url?scp=44649173243&partnerID=8YFLogxK

U2 - 10.1112/blms/bdm056

DO - 10.1112/blms/bdm056

M3 - 文章

AN - SCOPUS:44649173243

SN - 0024-6093

VL - 39

SP - 731

EP - 740

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 5

ER -