Representations Of Algebraic Groups

Author: Jens Carsten Jantzen
Editor: American Mathematical Soc.
ISBN: 082184377X
File Size: 51,67 MB
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The present book, which is a revised edition of the author's book published in 1987 by Academic Press, is intended to give the reader an introduction to the theory of algebraic representations of reductive algebraic groups. To develop appropriate techniques, the first part of the book is an introduction to the general theory of representations of algebraic group schemes. Here the author describes, among others, such important basic notions as induction functor, cohomology, quotients, Frobenius kernels, and reduction mod $p$. The second part of the book is devoted to the representation theory of reductive algebraic groups. It includes such topics as the description of simple modules, vanishing theorems, the Borel-Bott-Weil theorem and Weyl's character formula, Schubert schemes and line bundles on them. For this revised edition the author added several chapters describing some later developments, among them Schur algebras, Lusztig's conjecture, and Kazhdan-Lusztig polynomials, tilting modules, and representations of quantum groups.

Linear Algebraic Groups

Author: James E. Humphreys
Editor: Springer Science & Business Media
ISBN: 1468494430
File Size: 12,46 MB
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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.

Algebraic Groups

Author: J. S. Milne
Editor: Cambridge University Press
ISBN: 1107167485
File Size: 79,85 MB
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Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.

Linear Algebraic Groups

Author: T.A. Springer
Editor: Springer Science & Business Media
ISBN: 0817648402
File Size: 60,48 MB
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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.

Algebraic Groups

Author: Source Wikipedia
Editor: University-Press.org
ISBN: 9781230599281
File Size: 47,45 MB
Format: PDF
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 32. Chapters: (B, N) pair, Adelic algebraic group, Algebraic torus, Approximation in algebraic groups, Arithmetic group, Borel subgroup, Bruhat decomposition, Cartan subgroup, Diagonalizable group, Dieudonne module, Differential algebraic group, Differential Galois theory, E6 (mathematics), E7 (mathematics), E8 (mathematics), Etale group scheme, F4 (mathematics), Formal group, Fundamental lemma (Langlands program), G2 (mathematics), Geometric invariant theory, Glossary of algebraic groups, Group of Lie type, Hochschild-Mostow group, Hyperspecial subgroup, Inner form, Iwahori subgroup, Jordan-Chevalley decomposition, Kazhdan-Lusztig polynomial, Kneser-Tits conjecture, Kostant polynomial, Langlands decomposition, Lang-Steinberg theorem, Lattice (discrete subgroup), Lazard's universal ring, Linear algebraic group, Mirabolic group, Mumford-Tate group, Pseudo-reductive group, Quasi-split group, Radical of an algebraic group, Restricted Lie algebra, Root datum, Semisimple algebraic group, Severi-Brauer variety, Siegel parabolic subgroup, Special group (algebraic group theory), Springer resolution, Tannakian category, Unipotent, Weil conjecture on Tamagawa numbers, Weyl module, Witt vector.

Endomorphisms Of Linear Algebraic Groups

Author: Robert Steinberg
Editor: American Mathematical Soc.
ISBN: 0821812807
File Size: 80,55 MB
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Linear Algebraic Groups And Finite Groups Of Lie Type

Author: Gunter Malle
Editor: Cambridge University Press
ISBN: 113949953X
File Size: 63,89 MB
Format: PDF
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Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces more specialized topics in the subgroup structure of semisimple groups and describes the classification of the maximal subgroups of the simple algebraic groups. The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing textbooks. The authors provide numerous instructive exercises and examples for those who are learning the subject as well as more advanced topics for research students working in related areas.

Algebraic Groups And Their Birational Invariants

Author: V. E. Voskresenskii
Editor: American Mathematical Soc.
ISBN: 0821872885
File Size: 43,49 MB
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Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, $R$-equivalence, projective toric varieties, invariants of finite transformation groups, and index-formulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading.

Differential Algebra Algebraic Groups

Author:
Editor: Academic Press
ISBN: 9780080873695
File Size: 11,30 MB
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Differential Algebra & Algebraic Groups

Algebraic Groups And Number Theory

Author: Vladimir Platonov
Editor: Academic Press
ISBN: 9780080874593
File Size: 11,25 MB
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This milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number theory. The exposition of the topic is built on a synthesis of methods from algebraic geometry, number theory, analysis, and topology, and the result is a systematic overview ofalmost all of the major results of the arithmetic theory of algebraic groups obtained to date.

Conjugacy Classes In Semisimple Algebraic Groups

Author: James E. Humphreys
Editor: American Mathematical Soc.
ISBN: 0821852760
File Size: 73,62 MB
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The book provides a useful exposition of results on the structure of semisimple algebraic groups over an arbitrary algebraically closed field. After the fundamental work of Borel and Chevalley in the 1950s and 1960s, further results were obtained over the next thirty years on conjugacy classes and centralizers of elements of such groups. A reader-friendly volume which will be very useful to those wishing to know more about the structure of algebraic groups ... contains both a straightforward guide to the simpler ideas in the subject, and also a fascinating glimpse into some of the more abstruse areas which are the subject of current investigation. --Bulletin of the LMS

Differential Algebraic Groups

Author: Ellis Robert Kolchin
Editor: Academic Pr
ISBN:
File Size: 18,71 MB
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Algebraic Groups And Discontinuous Subgroups

Author:
Editor:
ISBN:
File Size: 66,44 MB
Format: PDF
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Representation Theory Of Algebraic Groups And Quantum Groups

Author: Akihiko Gyoja
Editor: Springer Science & Business Media
ISBN: 9780817646974
File Size: 53,22 MB
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Invited articles by top notch experts Focus is on topics in representation theory of algebraic groups and quantum groups Of interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics

Introduction To Affine Algebraic Groups

Author:
Editor:
ISBN:
File Size: 80,22 MB
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An Introduction To Algebraic Geometry And Algebraic Groups

Author: Meinolf Geck
Editor: Clarendon Press
ISBN: 0191663727
File Size: 45,62 MB
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An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles. Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type. The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields. Experts in the field will enjoy some of the new approaches to classical results. The text uses algebraic groups as the main examples, including worked out examples, instructive exercises, as well as bibliographical and historical remarks.

Trialitarian Algebraic Groups

Author: Skip Garibaldi
Editor:
ISBN:
File Size: 51,72 MB
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