Exponent reduction for projective Schur algebras

Eli Aljadeff*, Jack Sonn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper it is proved that the "exponent reduction property" holds for all projective Schur algebras. This was proved in an earlier paper of the authors for a special class, the "radical abelian algebras." The precise statement is as follows: let A be a projective Schur algebra over a field k and let k(μ) denote the maximal cyclotomic extension of k. If m is the exponent of A⊗kk(μ), then k contains a primitive mth root of unity. One corollary of this result is a negative answer to the question of whether or not the projective Schur group PS(k) is always equal to Br(L/k), where L is the composite of the maximal cyclotomic extension of k and the maximal Kummer extension of k. A second consequence is a proof of the "Brauer-Witt analogue" in characteristic p: if char(k)=p≠0, then every projective Schur algebra over k is Brauer equivalent to a radical abelian algebra.

Original languageEnglish
Pages (from-to)356-364
Number of pages9
JournalJournal of Algebra
Volume239
Issue number1
DOIs
StatePublished - 1 May 2001
Externally publishedYes

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