β Scribed by R. W. Carter (auth.), A. I. Kostrikin, I. R. Shafarevich (eds.)
No coin nor oath required. For personal study only.
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.
Front Matter....Pages i-vii
On the Representation Theory of the Finite Groups of Lie Type over an Algebraically Closed Field of Characteristic 0....Pages 1-120
Finite-Dimensional Division Algebras....Pages 121-233
Back Matter....Pages 235-243
Group Theory and Generalizations; K-Theory; Number Theory; Algebraic Geometry
π SIMILAR VOLUMES
The first contribution by Carter covers the theory of finite groups of Lie type, an important field of current mathematical research. In the second part, Platonov and Yanchevskii survey the structure of finite-dimensional division algebras, including an account of reduced K-theory.
This monograph contains two self-contained surveys of key aspects of algebra, complete with definitions and simple properties and references to proofs in the literature. The book will be of great interest to graduate students and researchers in mathematics, computer science and theoretical physics
Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces mo