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Author: T. Kambayashi
Publisher: Springer
ISBN: 3540372652
Category : Mathematics
Languages : en
Pages : 171
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Book Description
Author: T. Kambayashi
Publisher: Springer
ISBN: 3540372652
Category : Mathematics
Languages : en
Pages : 171
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Book Description
Author: Martin W. Liebeck
Publisher: American Mathematical Soc.
ISBN: 0821869205
Category : Mathematics
Languages : en
Pages : 394
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Book Description
This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of centralizers.
Author: J. S. Milne
Publisher: Cambridge University Press
ISBN: 1107167485
Category : Mathematics
Languages : en
Pages : 665
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Book Description
Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.
Author: T Kambayashi
Publisher: Springer
ISBN: 9783662171615
Category :
Languages : en
Pages : 180
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Book Description
Author: Alfonso Di Bartolo
Publisher: Springer
ISBN: 3540785841
Category : Mathematics
Languages : en
Pages : 223
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Book Description
Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups and Lie groups having only few subgroups or few factor groups of different type. In particular, the diversity of the nature of algebraic groups over fields of positive characteristic and over fields of characteristic zero is emphasized. This is revealed by the plethora of three-dimensional unipotent algebraic groups over a perfect field of positive characteristic, as well as, by many concrete examples which cover an area systematically. In the final section, algebraic groups and Lie groups having many closed normal subgroups are determined.
Author: Jens Carsten Jantzen
Publisher: American Mathematical Soc.
ISBN: 082184377X
Category : Mathematics
Languages : en
Pages : 594
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Book Description
Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
Author:
Publisher:
ISBN:
Category : Commutative rings
Languages : en
Pages : 165
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Book Description
Author: R. Steinberg
Publisher: Springer
ISBN: 3540379312
Category : Mathematics
Languages : en
Pages : 166
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Book Description
Author: James E. Humphreys
Publisher: Springer Science & Business Media
ISBN: 1468494430
Category : Mathematics
Languages : en
Pages : 259
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Book Description
James E. Humphreys is a distinguished Professor of Mathematics at the University of Massachusetts at Amherst. He has previously held posts at the University of Oregon and New York University. His main research interests include group theory and Lie algebras, and this graduate level text is an exceptionally well-written introduction to everything about linear algebraic groups.
Author: T.A. Springer
Publisher: Springer Science & Business Media
ISBN: 0817648402
Category : Mathematics
Languages : en
Pages : 347
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Book Description
The first edition of this book presented the theory of linear algebraic groups over an algebraically closed field. The second edition, thoroughly revised and expanded, extends the theory over arbitrary fields, which are not necessarily algebraically closed. It thus represents a higher aim. As in the first edition, the book includes a self-contained treatment of the prerequisites from algebraic geometry and commutative algebra, as well as basic results on reductive groups. As a result, the first part of the book can well serve as a text for an introductory graduate course on linear algebraic groups.
