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TitleAlgebra IX [electronic resource] : Finite Groups of Lie Type Finite-Dimensional Division Algebras / edited by A. I. Kostrikin, I. R. Shafarevich
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1996
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Descript VIII, 240 p. online resource


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


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

Mathematics Algebra Algebraic geometry Group theory K-theory Number theory Mathematics Group Theory and Generalizations Algebra K-Theory Number Theory Algebraic Geometry


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