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Algebra IX: Finite Groups of Lie Type Finite-Dimensional Division Algebras de A.I. Kostrikin

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

Editat de A.I. Kostrikin Traducere de P. M. Cohn Contribuţii de R.W. Carter Editat de I.R. Shafarevich Contribuţii de V.P. Platonov, V.I. Yanchevskii
en Limba Engleză Hardback – dec 1995
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.
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Specificații

ISBN-13: 9783540570387
ISBN-10: 3540570381
Pagini: 256
Ilustrații: VIII, 240 p.
Dimensiuni: 155 x 235 x 19 mm
Greutate: 0.54 kg
Ediția:1996
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Encyclopaedia of Mathematical Sciences

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

I. On the Representation Theory of the Finite Groups of Lie Type over an Algebraically Closed Field of Characteristic O.- II. Finite-Dimensional Division Algebras.- Author Index.

Textul de pe ultima copertă

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.