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Algebra IX: Finite Groups of Lie Type Finite-Dimensional Division Algebras

Algebra IX: Finite Groups of Lie Type Finite-Dimensional Division Algebras
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Dewey Class 512.2
Title Algebra IX ([EBook]) : Finite Groups of Lie Type Finite-Dimensional Division Algebras / edited by A. I. Kostrikin, I. R. Shafarevich.
Added Personal Name Kostrikin, Aleksei Ivanovic
Shafarevich, Igor R.(Igor Rostislavovich) , 1923-2017
Other name(s) SpringerLink (Online service)
Publication Berlin, Heidelberg : Springer , 1996.
Physical Details VIII, 240 pages : online resource.
Series Encyclopaedia of mathematical sciences 0938-0396 ; ; 77
ISBN 9783662032350
Summary Note 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.:
Contents note 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.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
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