Algebraic Groups And Lie Groups

Algebraic Groups And Lie Groups Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Algebraic Groups And Lie Groups book. This book definitely worth reading, it is an incredibly well-written.

Lie Groups and Algebraic Groups

Arkadij L. Onishchik,Ernest B. Vinberg
Lie Groups and Algebraic Groups Book PDF

Author : Arkadij L. Onishchik,Ernest B. Vinberg
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642743344

Get Book

Lie Groups and Algebraic Groups by Arkadij L. Onishchik,Ernest B. Vinberg Pdf

This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68. Our guiding idea was to present in the most economic way the theory of semisimple Lie groups on the basis of the theory of algebraic groups. Our main sources were A. Borel's paper [34], C. ChevalIey's seminar [14], seminar "Sophus Lie" [15] and monographs by C. Chevalley [4], N. Jacobson [9] and J-P. Serre [16, 17]. In preparing this book we have completely rearranged these notes and added two new chapters: "Lie groups" and "Real semisimple Lie groups". Several traditional topics of Lie algebra theory, however, are left entirely disregarded, e.g. universal enveloping algebras, characters of linear representations and (co)homology of Lie algebras. A distinctive feature of this book is that almost all the material is presented as a sequence of problems, as it had been in the first draft of the seminar's notes. We believe that solving these problems may help the reader to feel the seminar's atmosphere and master the theory. Nevertheless, all the non-trivial ideas, and sometimes solutions, are contained in hints given at the end of each section. The proofs of certain theorems, which we consider more difficult, are given directly in the main text. The book also contains exercises, the majority of which are an essential complement to the main contents.

Lie Groups and Algebraic Groups

Arkadij L. Onishchik,Ernest B. Vinberg
Lie Groups and Algebraic Groups Book PDF

Author : Arkadij L. Onishchik,Ernest B. Vinberg
Publisher : Springer
Page : 0 pages
File Size : 49,5 Mb
Release : 2011-12-06
Category : Mathematics
ISBN : 3642743366

Get Book

Lie Groups and Algebraic Groups by Arkadij L. Onishchik,Ernest B. Vinberg Pdf

This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68. Our guiding idea was to present in the most economic way the theory of semisimple Lie groups on the basis of the theory of algebraic groups. Our main sources were A. Borel's paper [34], C. ChevalIey's seminar [14], seminar "Sophus Lie" [15] and monographs by C. Chevalley [4], N. Jacobson [9] and J-P. Serre [16, 17]. In preparing this book we have completely rearranged these notes and added two new chapters: "Lie groups" and "Real semisimple Lie groups". Several traditional topics of Lie algebra theory, however, are left entirely disregarded, e.g. universal enveloping algebras, characters of linear representations and (co)homology of Lie algebras. A distinctive feature of this book is that almost all the material is presented as a sequence of problems, as it had been in the first draft of the seminar's notes. We believe that solving these problems may help the reader to feel the seminar's atmosphere and master the theory. Nevertheless, all the non-trivial ideas, and sometimes solutions, are contained in hints given at the end of each section. The proofs of certain theorems, which we consider more difficult, are given directly in the main text. The book also contains exercises, the majority of which are an essential complement to the main contents.

Lie Algebras and Algebraic Groups

Patrice Tauvel,Rupert W. T. Yu
Lie Algebras and Algebraic Groups Book PDF

Author : Patrice Tauvel,Rupert W. T. Yu
Publisher : Springer Science & Business Media
Page : 676 pages
File Size : 55,9 Mb
Release : 2005-04-25
Category : Mathematics
ISBN : 3540241701

Get Book

Lie Algebras and Algebraic Groups by Patrice Tauvel,Rupert W. T. Yu Pdf

Devoted to the theory of Lie algebras and algebraic groups, this book includes a large amount of commutative algebra and algebraic geometry so as to make it as self-contained as possible. The aim of the book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero. Detailed proofs are included, and some recent results are discussed in the final chapters.

Essays in the History of Lie Groups and Algebraic Groups

Armand Borel
Essays in the History of Lie Groups and Algebraic Groups Book PDF

Author : Armand Borel
Publisher : American Mathematical Soc.
Page : 184 pages
File Size : 55,9 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821802885

Get Book

Essays in the History of Lie Groups and Algebraic Groups by Armand Borel Pdf

Algebraic groups and Lie groups are important in most major areas of mathematics, occuring in diverse roles such as the symmetries of differential equations and as central figures in the Langlands program for number theory. In this book, Professor Borel looks at the development of the theory of Lie groups and algebraic groups, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. As the starting point of this passagefrom local to global, the author takes Lie's theory of local analytic transformation groups and Lie algebras. He then follows the globalization of the process in its two most important frameworks: (transcendental) differential geometry and algebraic geometry. Chapters II to IV are devoted to the former,Chapters V to VIII, to the latter.The essays in the first part of the book survey various proofs of the full reducibility of linear representations of $SL 2M$, the contributions H. Weyl to representation and invariant theory for Lie groups, and conclude with a chapter on E. Cartan's theory of symmetric spaces and Lie groups in the large.The second part of the book starts with Chapter V describing the development of the theory of linear algebraic groups in the 19th century. Many of the main contributions here are due to E. Study, E. Cartan, and above all, to L. Maurer. After being abandoned for nearly 50 years, the theory was revived by Chevalley and Kolchin and then further developed by many others. This is the focus of Chapter VI. The book concludes with two chapters on various aspects of the works of Chevalley on Lie groupsand algebraic groups and Kolchin on algebraic groups and the Galois theory of differential fields.The author brings a unique perspective to this study. As an important developer of some of the modern elements of both the differential geometric and the algebraic geometric sides of the theory, he has a particularly deep appreciation of the underlying mathematics. His lifelong involvement and his historical research in the subject give him a special appreciation of the story of its development.

p-Adic Lie Groups

Peter Schneider
p Adic Lie Groups Book PDF

Author : Peter Schneider
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 43,6 Mb
Release : 2011-06-11
Category : Mathematics
ISBN : 9783642211478

Get Book

p-Adic Lie Groups by Peter Schneider Pdf

Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with a self-contained and detailed introduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets up the analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition of Lazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the structure of completed group rings.

An Introduction to Lie Groups and Lie Algebras

Alexander A. Kirillov
An Introduction to Lie Groups and Lie Algebras Book PDF

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 48,7 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9780521889698

Get Book

An Introduction to Lie Groups and Lie Algebras by Alexander A. Kirillov Pdf

Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples

An Introduction to Algebraic Geometry and Algebraic Groups

Meinolf Geck
An Introduction to Algebraic Geometry and Algebraic Groups Book PDF

Author : Meinolf Geck
Publisher : Oxford University Press
Page : 321 pages
File Size : 46,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9780199676163

Get Book

An Introduction to Algebraic Geometry and Algebraic Groups by Meinolf Geck Pdf

An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.

Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras

Martin W. Liebeck,Gary M. Seitz
Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras Book PDF

Author : Martin W. Liebeck,Gary M. Seitz
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 44,5 Mb
Release : 2012-01-25
Category : Mathematics
ISBN : 9780821869208

Get Book

Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras by Martin W. Liebeck,Gary M. Seitz Pdf

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.

Lie Groups, Lie Algebras, and Representations

Brian Hall
Lie Groups Lie Algebras and Representations Book PDF

Author : Brian Hall
Publisher : Springer
Page : 452 pages
File Size : 54,7 Mb
Release : 2015-05-11
Category : Mathematics
ISBN : 9783319134673

Get Book

Lie Groups, Lie Algebras, and Representations by Brian Hall Pdf

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended. — The Mathematical Gazette

Representations of Algebraic Groups

Jens Carsten Jantzen
Representations of Algebraic Groups Book PDF

Author : Jens Carsten Jantzen
Publisher : American Mathematical Soc.
Page : 594 pages
File Size : 46,5 Mb
Release : 2003
Category : Linear algebraic groups
ISBN : 9780821843772

Get Book

Representations of Algebraic Groups by Jens Carsten Jantzen Pdf

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.

Linear Algebraic Groups and Finite Groups of Lie Type

Gunter Malle,Donna Testerman
Linear Algebraic Groups and Finite Groups of Lie Type Book PDF

Author : Gunter Malle,Donna Testerman
Publisher : Cambridge University Press
Page : 324 pages
File Size : 55,9 Mb
Release : 2011-09-08
Category : Mathematics
ISBN : 9781139499538

Get Book

Linear Algebraic Groups and Finite Groups of Lie Type by Gunter Malle,Donna Testerman Pdf

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.

Geometry of Lie Groups

B. Rosenfeld,Bill Wiebe
Geometry of Lie Groups Book PDF

Author : B. Rosenfeld,Bill Wiebe
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 50,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475753257

Get Book

Geometry of Lie Groups by B. Rosenfeld,Bill Wiebe Pdf

This book is the result of many years of research in Non-Euclidean Geometries and Geometry of Lie groups, as well as teaching at Moscow State University (1947- 1949), Azerbaijan State University (Baku) (1950-1955), Kolomna Pedagogical Col lege (1955-1970), Moscow Pedagogical University (1971-1990), and Pennsylvania State University (1990-1995). My first books on Non-Euclidean Geometries and Geometry of Lie groups were written in Russian and published in Moscow: Non-Euclidean Geometries (1955) [Ro1] , Multidimensional Spaces (1966) [Ro2] , and Non-Euclidean Spaces (1969) [Ro3]. In [Ro1] I considered non-Euclidean geometries in the broad sense, as geometry of simple Lie groups, since classical non-Euclidean geometries, hyperbolic and elliptic, are geometries of simple Lie groups of classes Bn and D , and geometries of complex n and quaternionic Hermitian elliptic and hyperbolic spaces are geometries of simple Lie groups of classes An and en. [Ro1] contains an exposition of the geometry of classical real non-Euclidean spaces and their interpretations as hyperspheres with identified antipodal points in Euclidean or pseudo-Euclidean spaces, and in projective and conformal spaces. Numerous interpretations of various spaces different from our usual space allow us, like stereoscopic vision, to see many traits of these spaces absent in the usual space.

Algebraic Groups and Lie Groups

Gus Lehrer,Alan L. Carey
Algebraic Groups and Lie Groups Book PDF

Author : Gus Lehrer,Alan L. Carey
Publisher : Cambridge University Press
Page : 396 pages
File Size : 50,7 Mb
Release : 1997-01-23
Category : Mathematics
ISBN : 0521585325

Get Book

Algebraic Groups and Lie Groups by Gus Lehrer,Alan L. Carey Pdf

This volume contains original research articles by many of the world's leading researchers in algebraic and Lie groups. Its inclination is algebraic and geometic, although analytical aspects are included. The central theme reflects the interests of R. W. Richardson, viz connections between representation theory and the structure and geometry of algebraic groups. All workers on algebraic and Lie groups will find that this book contains a wealth of interesting material.

Linear Algebraic Groups

Armand Borel
Linear Algebraic Groups Book PDF

Author : Armand Borel
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209416

Get Book

Linear Algebraic Groups by Armand Borel Pdf

This revised, enlarged edition of Linear Algebraic Groups (1969) starts by presenting foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. It then turns to solvable groups, general properties of linear algebraic groups, and Chevally’s structure theory of reductive groups over algebraically closed groundfields. It closes with a focus on rationality questions over non-algebraically closed fields.

Linear Algebraic Groups

James E. Humphreys
Linear Algebraic Groups Book PDF

Author : James E. Humphreys
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468494433

Get Book

Linear Algebraic Groups by James E. Humphreys Pdf

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.