Lie Groups Lie Algebras And Cohomology

Author : Anthony W. Knapp
Publisher : Princeton University Press
Page : 522 pages
File Size : 40,9 Mb
Release : 1988-05-21
Category : Mathematics
ISBN : 9780691084985

Get Book

Lie Groups, Lie Algebras, and Cohomology by Anthony W. Knapp Pdf

This book starts with the elementary theory of Lie groups of matrices and arrives at the definition, elementary properties, and first applications of cohomological induction, which is a recently discovered algebraic construction of group representations. Along the way it develops the computational techniques that are so important in handling Lie groups. The book is based on a one-semester course given at the State University of New York, Stony Brook in fall, 1986 to an audience having little or no background in Lie groups but interested in seeing connections among algebra, geometry, and Lie theory. These notes develop what is needed beyond a first graduate course in algebra in order to appreciate cohomological induction and to see its first consequences. Along the way one is able to study homological algebra with a significant application in mind; consequently one sees just what results in that subject are fundamental and what results are minor.

Author : Josi A. de Azcárraga,Josi M. Izquierdo
Publisher : Cambridge University Press
Page : 480 pages
File Size : 52,5 Mb
Release : 1998-08-06
Category : Mathematics
ISBN : 0521597005

Get Book

Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics by Josi A. de Azcárraga,Josi M. Izquierdo Pdf

A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.

Author : Anthony W. Knapp
Publisher : Princeton University Press
Page : 526 pages
File Size : 42,9 Mb
Release : 2021-01-12
Category : Mathematics
ISBN : 9780691223803

Get Book

Lie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34 by Anthony W. Knapp Pdf

This book starts with the elementary theory of Lie groups of matrices and arrives at the definition, elementary properties, and first applications of cohomological induction, which is a recently discovered algebraic construction of group representations. Along the way it develops the computational techniques that are so important in handling Lie groups. The book is based on a one-semester course given at the State University of New York, Stony Brook in fall, 1986 to an audience having little or no background in Lie groups but interested in seeing connections among algebra, geometry, and Lie theory. These notes develop what is needed beyond a first graduate course in algebra in order to appreciate cohomological induction and to see its first consequences. Along the way one is able to study homological algebra with a significant application in mind; consequently one sees just what results in that subject are fundamental and what results are minor.

Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
Page : 622 pages
File Size : 54,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475724530

Get Book

Lie Groups Beyond an Introduction by Anthony W. Knapp Pdf

Lie Groups Beyond an Introduction takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. A feature of the presentation is that it encourages the reader's comprehension of Lie group theory to evolve from beginner to expert: initial insights make use of actual matrices, while later insights come from such structural features as properties of root systems, or relationships among subgroups, or patterns among different subgroups.

Author : D B Fuks
Publisher : Unknown
Page : 352 pages
File Size : 55,8 Mb
Release : 1986-12-31
Category : Electronic
ISBN : 1468487663

Get Book

Cohomology of Infinite-Dimensional Lie Algebras by D B Fuks Pdf

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 55,5 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

Author : José Adolfo de Azcárraga,José M. Izquierdo
Publisher : Unknown
Page : 455 pages
File Size : 50,9 Mb
Release : 1995
Category : Electronic
ISBN : OCLC:468375905

Get Book

Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics by José Adolfo de Azcárraga,José M. Izquierdo Pdf

Author : V.S. Varadarajan
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 49,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781461211266

Get Book

Lie Groups, Lie Algebras, and Their Representations by V.S. Varadarajan Pdf

This book has grown out of a set of lecture notes I had prepared for a course on Lie groups in 1966. When I lectured again on the subject in 1972, I revised the notes substantially. It is the revised version that is now appearing in book form. The theory of Lie groups plays a fundamental role in many areas of mathematics. There are a number of books on the subject currently available -most notably those of Chevalley, Jacobson, and Bourbaki-which present various aspects of the theory in great depth. However, 1 feei there is a need for a single book in English which develops both the algebraic and analytic aspects of the theory and which goes into the representation theory of semi simple Lie groups and Lie algebras in detail. This book is an attempt to fiii this need. It is my hope that this book will introduce the aspiring graduate student as well as the nonspecialist mathematician to the fundamental themes of the subject. I have made no attempt to discuss infinite-dimensional representations. This is a very active field, and a proper treatment of it would require another volume (if not more) of this size. However, the reader who wants to take up this theory will find that this book prepares him reasonably well for that task.

Author : A.L. Onishchik
Publisher : Boom Koninklijke Uitgevers
Page : 238 pages
File Size : 50,7 Mb
Release : 2000-02-03
Category : Mathematics
ISBN : 3540505857

Get Book

Lie Groups and Lie Algebras II by A.L. Onishchik Pdf

A systematic survey of all the basic results on the theory of discrete subgroups of Lie groups, presented in a convenient form for users. The book makes the theory accessible to a wide audience, and will be a standard reference for many years to come.

Author : Daniel Bump
Publisher : Springer Science & Business Media
Page : 551 pages
File Size : 54,5 Mb
Release : 2013-10-01
Category : Mathematics
ISBN : 9781461480242

Get Book

Lie Groups by Daniel Bump Pdf

This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range of material to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests. This second edition has substantial new material, including improved discussions of underlying principles, streamlining of some proofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the Peter–Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl group, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics that are treated are symmetric function theory, the representation theory of the symmetric group, Frobenius–Schur duality and GL(n) × GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the "philosophy of cusp forms" and the cohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations.

Author : B.P. Komrakov,I.S. Krasil'shchik,G.L. Litvinov,A.B. Sossinsky
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401152587

Get Book

Lie Groups and Lie Algebras by B.P. Komrakov,I.S. Krasil'shchik,G.L. Litvinov,A.B. Sossinsky Pdf

This collection contains papers conceptually related to the classical ideas of Sophus Lie (i.e., to Lie groups and Lie algebras). Obviously, it is impos sible to embrace all such topics in a book of reasonable size. The contents of this one reflect the scientific interests of those authors whose activities, to some extent at least, are associated with the International Sophus Lie Center. We have divided the book into five parts in accordance with the basic topics of the papers (although it can be easily seen that some of them may be attributed to several parts simultaneously). The first part (quantum mathematics) combines the papers related to the methods generated by the concepts of quantization and quantum group. The second part is devoted to the theory of hypergroups and Lie hypergroups, which is one of the most important generalizations of the classical concept of locally compact group and of Lie group. A natural harmonic analysis arises on hypergroups, while any abstract transformation of Fourier type is gen erated by some hypergroup (commutative or not). Part III contains papers on the geometry of homogeneous spaces, Lie algebras and Lie superalgebras. Classical problems of the representation theory for Lie groups, as well as for topological groups and semigroups, are discussed in the papers of Part IV. Finally, the last part of the collection relates to applications of the ideas of Sophus Lie to differential equations.

Author : Claude Chevalley
Publisher : Courier Dover Publications
Page : 227 pages
File Size : 46,8 Mb
Release : 2018-03-21
Category : Mathematics
ISBN : 9780486824536

Get Book

Theory of Lie Groups by Claude Chevalley Pdf

The standard text on the subject for many years, this introductory treatment covers classical linear groups, topological groups, manifolds, analytic groups, differential calculus of Cartan, and compact Lie groups and their representations. 1946 edition.

Author : Shrawan Kumar
Publisher : Springer Science & Business Media
Page : 613 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201052

Get Book

Kac-Moody Groups, their Flag Varieties and Representation Theory by Shrawan Kumar Pdf

Kac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alge bras which we refer to as the finite case. The theory has undergone tremendous developments in various directions and connections with diverse areas abound, including mathematical physics, so much so that this theory has become a stan dard tool in mathematics. A detailed treatment of the Lie algebra aspect of the theory can be found in V. Kac's book [Kac-90l This self-contained work treats the algebro-geometric and the topological aspects of Kac-Moody theory from scratch. The emphasis is on the study of the Kac-Moody groups 9 and their flag varieties XY, including their detailed construction, and their applications to the representation theory of g. In the finite case, 9 is nothing but a semisimple Y simply-connected algebraic group and X is the flag variety 9 /Py for a parabolic subgroup p y C g.

Author : Melvin Hausner,Jacob T. Schwartz
Publisher : CRC Press
Page : 242 pages
File Size : 51,5 Mb
Release : 1968
Category : Lie algebras
ISBN : 9780677002804

Get Book

Lie Groups, Lie Algebras by Melvin Hausner,Jacob T. Schwartz Pdf

Polished lecture notes provide a clean and usefully detailed account of the standard elements of the theory of Lie groups and algebras. Following nineteen pages of preparatory material, Part I (seven brief chapters) treats "Lie groups and their Lie algebras"; Part II (seven chapters) treats "complex semi-simple Lie algebras"; Part III (two chapters) treats "real semi-simple Lie algebras". The page design is intimidatingly dense, the exposition very much in the familiar "definition/lemma/proof/theorem/proof/remark" mode, and there are no exercises or bibliography. (NW) Annotation copyrighted by Book News, Inc., Portland, OR

Author : Victor Kac
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211044

Get Book

Infinite Dimensional Groups with Applications by Victor Kac Pdf

This volume records most of the talks given at the Conference on Infinite-dimensional Groups held at the Mathematical Sciences Research Institute at Berkeley, California, May 10-May 15, 1984, as a part of the special program on Kac-Moody Lie algebras. The purpose of the conference was to review recent developments of the theory of infinite-dimensional groups and its applications. The present collection concentrates on three very active, interrelated directions of the field: general Kac-Moody groups, gauge groups (especially loop groups) and diffeomorphism groups. I would like to express my thanks to the MSRI for sponsoring the meeting, to Ms. Faye Yeager for excellent typing, to the authors for their manuscripts, and to Springer-Verlag for publishing this volume. V. Kac INFINITE DIMENSIONAL GROUPS WITH APPLICATIONS CONTENTS The Lie Group Structure of M. Adams. T. Ratiu 1 Diffeomorphism Groups and & R. Schmid Invertible Fourier Integral Operators with Applications On Landau-Lifshitz Equation and E. Date 71 Infinite Dimensional Groups Flat Manifolds and Infinite D. S. Freed 83 Dimensional Kahler Geometry Positive-Energy Representations R. Goodman 125 of the Group of Diffeomorphisms of the Circle Instantons and Harmonic Maps M. A. Guest 137 A Coxeter Group Approach to Z. Haddad 157 Schubert Varieties Constructing Groups Associated to V. G. Kac 167 Infinite-Dimensional Lie Algebras I. Kaplansky 217 Harish-Chandra Modules Over the Virasoro Algebra & L. J. Santharoubane 233 Rational Homotopy Theory of Flag S.