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Lie Groups, Lie Algebras, and Representations
An Elementary Introduction
Buch von Brian Hall
Sprache: Englisch

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Beschreibung
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
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
Über den Autor
Brian Hall is Professor of Mathematics at the University of Notre Dame, IN.
Zusammenfassung

New edition extensively revised and updated

Covers the core topics of Lie theory from an elementary point of view

Includes many new exercises

Inhaltsverzeichnis
Part I: General Theory.-Matrix Lie Groups.- The Matrix Exponential.- Lie Algebras.- Basic Representation Theory.- The Baker-Campbell-Hausdorff Formula and its Consequences.- Part II: Semisimple Lie Algebras.- The Representations of sl(3;C).-Semisimple Lie Algebras.- Root Systems.- Representations of Semisimple Lie Algebras.- Further Properties of the Representations.- Part III: Compact lie Groups.- Compact Lie Groups and Maximal Tori.- The Compact Group Approach to Representation Theory.- Fundamental Groups of Compact Lie Groups.- Appendices.
Details
Erscheinungsjahr: 2015
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 449
Reihe: Graduate Texts in Mathematics
Inhalt: xiii
449 S.
72 s/w Illustr.
7 farbige Illustr.
449 p. 79 illus.
7 illus. in color.
ISBN-13: 9783319134666
ISBN-10: 3319134663
Sprache: Englisch
Herstellernummer: 86385207
Einband: Gebunden
Autor: Hall, Brian
Auflage: 2nd ed. 2015
Hersteller: Springer-Verlag GmbH
Springer International Publishing
Abbildungen: 20 farbige Abbildungen, Bibliographie
Maße: 241 x 162 x 30 mm
Von/Mit: Brian Hall
Erscheinungsdatum: 22.05.2015
Gewicht: 0,937 kg
preigu-id: 105040500
Über den Autor
Brian Hall is Professor of Mathematics at the University of Notre Dame, IN.
Zusammenfassung

New edition extensively revised and updated

Covers the core topics of Lie theory from an elementary point of view

Includes many new exercises

Inhaltsverzeichnis
Part I: General Theory.-Matrix Lie Groups.- The Matrix Exponential.- Lie Algebras.- Basic Representation Theory.- The Baker-Campbell-Hausdorff Formula and its Consequences.- Part II: Semisimple Lie Algebras.- The Representations of sl(3;C).-Semisimple Lie Algebras.- Root Systems.- Representations of Semisimple Lie Algebras.- Further Properties of the Representations.- Part III: Compact lie Groups.- Compact Lie Groups and Maximal Tori.- The Compact Group Approach to Representation Theory.- Fundamental Groups of Compact Lie Groups.- Appendices.
Details
Erscheinungsjahr: 2015
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 449
Reihe: Graduate Texts in Mathematics
Inhalt: xiii
449 S.
72 s/w Illustr.
7 farbige Illustr.
449 p. 79 illus.
7 illus. in color.
ISBN-13: 9783319134666
ISBN-10: 3319134663
Sprache: Englisch
Herstellernummer: 86385207
Einband: Gebunden
Autor: Hall, Brian
Auflage: 2nd ed. 2015
Hersteller: Springer-Verlag GmbH
Springer International Publishing
Abbildungen: 20 farbige Abbildungen, Bibliographie
Maße: 241 x 162 x 30 mm
Von/Mit: Brian Hall
Erscheinungsdatum: 22.05.2015
Gewicht: 0,937 kg
preigu-id: 105040500
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