Algebra IX

Finite Groups of Lie Type Finite-Dimensional Division Algebras

  • A. I. Kostrikin
  • I. R. Shafarevich

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 77)

Table of contents

  1. Front Matter
    Pages i-vii
  2. V. P. Platonov, V. I. Yanchevskii
    Pages 121-233
  3. Back Matter
    Pages 235-243

About this book

Introduction

The finite groups of Lie type are of central mathematical importance and the problem of understanding their irreducible representations is of great interest. The representation theory of these groups over an algebraically closed field of characteristic zero was developed by P.Deligne and G.Lusztig in 1976 and subsequently in a series of papers by Lusztig culminating in his book in 1984. The purpose of the first part of this book is to give an overview of the subject, without including detailed proofs. The second part is a survey of the structure of finite-dimensional division algebras with many outline proofs, giving the basic theory and methods of construction and then goes on to a deeper analysis of division algebras over valuated fields. An account of the multiplicative structure and reduced K-theory presents recent work on the subject, including that of the authors. Thus it forms a convenient and very readable introduction to a field which in the last two decades has seen much progress.

Keywords

Algebra Brauer group Brauersche Gruppe Cohomology Darstellungen Divisionsalgebra Gruppen vom Lieschen Typ Representation theory division algebra endliche Gruppen finite groups groups of Lie type representations

Editors and affiliations

  • A. I. Kostrikin
    • 1
  • I. R. Shafarevich
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03235-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1996
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08167-5
  • Online ISBN 978-3-662-03235-0
  • Series Print ISSN 0938-0396
  • About this book