Algebra IX: Finite Groups of Lie Type Finite-Dimensional Division Algebras: 77 (Encyclopaedia of Mathematical Sciences, 77) - Hardcover

Hardcover

ISBN 10: 3540570381 ISBN 13: 9783540570387

Publisher: Springer, 1995

Synopsis

The first contribution covers the theory of finite groups of Lie type, which is an important field of current mathematical research. After giving the basic information Carter describes the Deligne-Lusztig method of obtaining characters of these groups using l-adic cohomology and subsequent work of Lusztig.
The second part by Platonov and Yanchevskii surveys the structure of finite-dimensional division algebras and includes an account of reduced K-theory.

About this title

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 1995
• Language: English
• ISBN 10: 3540570381
• ISBN 13: 9783540570387
• Binding: Hardcover
• Number of pages: 248
• Editor: Kostrikin A.I., Shafarevich I.R.