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Algebra: 9 Finite groups of Lie Type

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 i...

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Weitere Verfasser:	Kostrikin, Aleksej I. 1929-2000 (HerausgeberIn), Šafarevič, Igorʹ R. 1923-2017 (HerausgeberIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Berlin Springer-Verlag Berlin Heidelberg GmbH [1996]
Schriftenreihe:	Encyclopaedia of mathematical sciences volume 77
Schlagworte:	Mathematics Geometry, algebraic Group theory K-theory Group Theory and Generalizations K-Theory Number theory Algebraic Geometry Mathematik
Online-Zugang:	BTU01 TUM01 UBA01 UBT01 Volltext
Zusammenfassung:	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.
Beschreibung:	1 Online-Ressource (viii, 240 Seiten)
ISBN:	9783662032350
DOI:	10.1007/978-3-662-03235-0

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index_date	2024-07-03T16:45:16Z
indexdate	2024-07-10T09:04:49Z
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isbn	9783662032350
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spelling	Kostrikin, Aleksej I. 1929-2000 (DE-588)1028287658 edt Algebra Algebra 9 Finite groups of Lie Type A.I. Kostrikin, l.R. Shafarevich (eds.) Berlin Springer-Verlag Berlin Heidelberg GmbH [1996] 1 Online-Ressource (viii, 240 Seiten) txt rdacontent c rdamedia cr rdacarrier Encyclopaedia of mathematical sciences volume 77 Encyclopaedia of mathematical sciences 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. Mathematics Geometry, algebraic Group theory K-theory Group Theory and Generalizations K-Theory Number theory Algebraic Geometry Mathematik Šafarevič, Igorʹ R. 1923-2017 (DE-588)119280337 edt (DE-604)BV047175815 9 Erscheint auch als Druck-Ausgabe 978-3-642-08167-5 Encyclopaedia of mathematical sciences volume 77 (DE-604)BV035421342 77 https://doi.org/10.1007/978-3-662-03235-0 Verlag URL des Erstveröffentlichers Volltext Finite-dimensional division algebras
spellingShingle	Algebra Encyclopaedia of mathematical sciences Mathematics Geometry, algebraic Group theory K-theory Group Theory and Generalizations K-Theory Number theory Algebraic Geometry Mathematik
title	Algebra
title_alt	Algebra
title_auth	Algebra
title_exact_search	Algebra
title_exact_search_txtP	Algebra
title_full	Algebra 9 Finite groups of Lie Type A.I. Kostrikin, l.R. Shafarevich (eds.)
title_fullStr	Algebra 9 Finite groups of Lie Type A.I. Kostrikin, l.R. Shafarevich (eds.)
title_full_unstemmed	Algebra 9 Finite groups of Lie Type A.I. Kostrikin, l.R. Shafarevich (eds.)
title_short	Algebra
title_sort	algebra finite groups of lie type
topic	Mathematics Geometry, algebraic Group theory K-theory Group Theory and Generalizations K-Theory Number theory Algebraic Geometry Mathematik
topic_facet	Mathematics Geometry, algebraic Group theory K-theory Group Theory and Generalizations K-Theory Number theory Algebraic Geometry Mathematik
url	https://doi.org/10.1007/978-3-662-03235-0
volume_link	(DE-604)BV047175815 (DE-604)BV035421342
work_keys_str_mv	AT kostrikinalekseji algebra AT safarevicigorʹr algebra AT kostrikinalekseji algebra9 AT safarevicigorʹr algebra9

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