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Bulletin of the London Mathematical Society Advance Access originally published online on August 22, 2007
Bulletin of the London Mathematical Society 2007 39(5):731-740; doi:10.1112/blms/bdm056
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© 2007 London Mathematical Society

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

Eli Aljadeff

Department of Mathematics
Technion-Israel Institute of Technology
32000 Haifa
Israel

Ángel Del Río

Departamento de Matemáticas
Universidad de Murcia
30100 Murcia
Spain
adelrio{at}um.es

Received 26 August 2006.

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.

2000 Mathematics Subject Classification 20C25, 16K50.

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.


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