Lie Groups, Lie Algebras, and Cohomology

Lie Groups, Lie Algebras, and Cohomology PDF

Author: Anthony W. Knapp

Publisher: Princeton University Press

Published: 1988-05-21

Total Pages: 522

ISBN-13: 069108498X

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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.

Lie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34

Lie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34 PDF

Author: Anthony W. Knapp

Publisher: Princeton University Press

Published: 2021-01-12

Total Pages: 526

ISBN-13: 0691223807

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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.

Lie Groups Beyond an Introduction

Lie Groups Beyond an Introduction PDF

Author: Anthony W. Knapp

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 622

ISBN-13: 1475724535

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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.

Lie Groups, Lie Algebras, and Some of Their Applications

Lie Groups, Lie Algebras, and Some of Their Applications PDF

Author: Robert Gilmore

Publisher: Courier Corporation

Published: 2012-05-23

Total Pages: 610

ISBN-13: 0486131564

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This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.

Lie Groups and Lie Algebras

Lie Groups and Lie Algebras PDF

Author: B.P. Komrakov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 442

ISBN-13: 9401152586

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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.

Lie Groups and Lie Algebras II

Lie Groups and Lie Algebras II PDF

Author: A.L. Onishchik

Publisher: Boom Koninklijke Uitgevers

Published: 2000-02-03

Total Pages: 238

ISBN-13: 9783540505853

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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.

Lie Groups

Lie Groups PDF

Author: Daniel Bump

Publisher: Springer Science & Business Media

Published: 2013-10-01

Total Pages: 532

ISBN-13: 1461480248

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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.

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