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＜電子ブック＞
Algebra IX : Finite Groups of Lie Type Finite-Dimensional Division Algebras / edited by A.I. Kostrikin, I.R. Shafarevich
(Encyclopaedia of Mathematical Sciences ; 77)

版	1st ed. 1996.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1996
本文言語	英語
大きさ	VIII, 240 p : online resource
著者標目	Kostrikin, A.I editor Shafarevich, I.R editor SpringerLink (Online service)
件　名	LCSH:Group theory LCSH:Algebra LCSH:K-theory LCSH:Number theory LCSH:Algebraic geometry FREE:Group Theory and Generalizations FREE:Algebra FREE:K-Theory FREE:Number Theory FREE:Algebraic Geometry
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-662-03235-0

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