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Every projective Schur algebra is Brauer equivalent to a radical abelian algebra
Author(s) -
Aljadeff Eli,
Río Ángel Del
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm056
Subject(s) - mathematics , brauer group , pure mathematics , division algebra , cellular algebra , schur algebra , abelian group , schur multiplier , conjecture , algebra over a field , filtered algebra , algebra representation , cyclic group , classical orthogonal polynomials , gegenbauer polynomials , orthogonal polynomials
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.