Algebra IX
Finite Groups of Lie Type Finite-Dimensional Division Algebras
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Beschreibung
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.
This book covers two important topics of current research in algebra. It addresses researchers and graduate students in mathematics.
Autor*in
A.I. Kostrikin
Themen in »Algebra IX«
Brauer group Brauersche Gruppe Cohomology Darstellungen Divisionsalgebra Gruppen vom Lieschen Typ Representation theory division algebra endliche Gruppen finite groups groups of Lie type representations