A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods

A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods

Author: Johan G. F. Belinfante

Publisher: SIAM

Published: 1989-01-01

Total Pages: 175

ISBN-13: 9781611971330

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Introduces the concepts and methods of the Lie theory in a form accessible to the non-specialist by keeping mathematical prerequisites to a minimum. Although the authors have concentrated on presenting results while omitting most of the proofs, they have compensated for these omissions by including many references to the original literature. Their treatment is directed toward the reader seeking a broad view of the subject rather than elaborate information about technical details. Illustrations of various points of the Lie theory itself are found throughout the book in material on applications. In this reprint edition, the authors have resisted the temptation of including additional topics. Except for correcting a few minor misprints, the character of the book, especially its focus on classical representation theory and its computational aspects, has not been changed.


Book Synopsis A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods by : Johan G. F. Belinfante

Download or read book A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods written by Johan G. F. Belinfante and published by SIAM. This book was released on 1989-01-01 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the concepts and methods of the Lie theory in a form accessible to the non-specialist by keeping mathematical prerequisites to a minimum. Although the authors have concentrated on presenting results while omitting most of the proofs, they have compensated for these omissions by including many references to the original literature. Their treatment is directed toward the reader seeking a broad view of the subject rather than elaborate information about technical details. Illustrations of various points of the Lie theory itself are found throughout the book in material on applications. In this reprint edition, the authors have resisted the temptation of including additional topics. Except for correcting a few minor misprints, the character of the book, especially its focus on classical representation theory and its computational aspects, has not been changed.

Lie Groups, Lie Algebras, and Cohomology

Lie Groups, Lie Algebras, and Cohomology

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.


Book Synopsis Lie Groups, Lie Algebras, and Cohomology by : Anthony W. Knapp

Download or read book Lie Groups, Lie Algebras, and Cohomology written by Anthony W. Knapp and published by Princeton University Press. This book was released on 1988-05-21 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Algebras: Applications and Computational Methods

Lie Algebras: Applications and Computational Methods

Author: Bernard Kolman

Publisher:

Published: 1973

Total Pages: 176

ISBN-13:

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Book Synopsis Lie Algebras: Applications and Computational Methods by : Bernard Kolman

Download or read book Lie Algebras: Applications and Computational Methods written by Bernard Kolman and published by . This book was released on 1973 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

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

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.


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

Download or read book Lie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34 written by Anthony W. Knapp and published by Princeton University Press. This book was released on 2021-01-12 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods

A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods

Author: Johan G. F. Belinfante

Publisher: SIAM

Published: 1989-01-01

Total Pages: 168

ISBN-13: 0898712432

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In this reprint edition, the character of the book, especially its focus on classical representation theory and its computational aspects, has not been changed


Book Synopsis A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods by : Johan G. F. Belinfante

Download or read book A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods written by Johan G. F. Belinfante and published by SIAM. This book was released on 1989-01-01 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this reprint edition, the character of the book, especially its focus on classical representation theory and its computational aspects, has not been changed

Lie Algebras : Applications and Computational Methods

Lie Algebras : Applications and Computational Methods

Author: Bernard Kolman

Publisher:

Published: 1974

Total Pages: 0

ISBN-13:

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Book Synopsis Lie Algebras : Applications and Computational Methods by : Bernard Kolman

Download or read book Lie Algebras : Applications and Computational Methods written by Bernard Kolman and published by . This book was released on 1974 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lie Algebras

Lie Algebras

Author: Bernard Kolman

Publisher: Society for Industrial and Applied Mathematics (SIAM)

Published: 1973-12

Total Pages: 155

ISBN-13: 9780898711530

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Book Synopsis Lie Algebras by : Bernard Kolman

Download or read book Lie Algebras written by Bernard Kolman and published by Society for Industrial and Applied Mathematics (SIAM). This book was released on 1973-12 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lie Groups and Lie Algebras

Lie Groups and Lie Algebras

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.


Book Synopsis Lie Groups and Lie Algebras by : B.P. Komrakov

Download or read book Lie Groups and Lie Algebras written by B.P. Komrakov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, Lie Algebras

Lie Groups, Lie Algebras

Author: Melvin Hausner

Publisher: CRC Press

Published: 1968

Total Pages: 242

ISBN-13: 0677002807

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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


Book Synopsis Lie Groups, Lie Algebras by : Melvin Hausner

Download or read book Lie Groups, Lie Algebras written by Melvin Hausner and published by CRC Press. This book was released on 1968 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Lie Theory

Lie Theory

Author: Jean-Philippe Anker

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 341

ISBN-13: 0817681922

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* First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.


Book Synopsis Lie Theory by : Jean-Philippe Anker

Download or read book Lie Theory written by Jean-Philippe Anker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: * First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.