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The Schur Subgroup of the Brauer Group

  • Alejandro Adem
  • R. James Milgram
Chapter
  • 316 Downloads
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 309)

Abstract

In this final chapter we apply the techniques of group cohomology to the representation theory of finite groups. Given G a finite group we know that ℙ(G) is semi-simple for any field of characteristic zero. Consequently, from the Wedderburn theorems there is a decomposition
$$F(G) = \sum {{M_{ni}}({D_i})} $$
(0.1)
where the D i run over central simple division algebras with center Ki a finite cyclotomic extension of F. The question that we answer here is the determination of all the classes {D i } ∊ B(F) which arise in this way, that is to say, which division algebras occur in the simple components of the group ring of a finite group.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Alejandro Adem
    • 1
  • R. James Milgram
    • 2
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.Department of Applied HomotopyStanford UniversityStanfordUSA

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