Graduate Texts in Mathematics

Lie Groups, Lie Algebras, and Representations

An Elementary Introduction

Autoren: Hall, Brian C.

  • New edition extensively revised and updated
  • Covers the core topics of Lie theory from an elementary point of view
  • Includes many new exercises
Weitere Vorteile

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eBook 51,16 €
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  • ISBN 978-3-319-13467-3
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Hardcover 64,19 €
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  • ISBN 978-3-319-13466-6
  • Kostenfreier Versand für Individualkunden weltweit
  • Gewöhnlich versandfertig in 3-5 Werktagen.
Softcover 64,19 €
Preis für Deutschland (Brutto)
  • ISBN 978-3-319-37433-8
  • Kostenfreier Versand für Individualkunden weltweit
  • Gewöhnlich versandfertig in 3-5 Werktagen.
Über dieses Lehrbuch

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

Über den Autor

Brian Hall is Professor of Mathematics at the University of Notre Dame, IN.

Stimmen zum Buch

“The first edition of this book was very good; the second is even better, and more versatile. This text remains one of the most attractive sources available from which to learn elementary Lie group theory, and is highly recommended.” (Mark Hunacek, The Mathematical Gazette, Vol. 101 (551), July, 2017)


Video

Inhaltsverzeichnis (14 Kapitel)

Dieses Buch kaufen

eBook 51,16 €
Preis für Deutschland (Brutto)
  • ISBN 978-3-319-13467-3
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: PDF, EPUB
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Hardcover 64,19 €
Preis für Deutschland (Brutto)
  • ISBN 978-3-319-13466-6
  • Kostenfreier Versand für Individualkunden weltweit
  • Gewöhnlich versandfertig in 3-5 Werktagen.
Softcover 64,19 €
Preis für Deutschland (Brutto)
  • ISBN 978-3-319-37433-8
  • Kostenfreier Versand für Individualkunden weltweit
  • Gewöhnlich versandfertig in 3-5 Werktagen.
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Bibliografische Information

Bibliographic Information
Buchtitel
Lie Groups, Lie Algebras, and Representations
Buchuntertitel
An Elementary Introduction
Autoren
Titel der Buchreihe
Graduate Texts in Mathematics
Buchreihen Band
222
Copyright
2015
Verlag
Springer International Publishing
Copyright Inhaber
Springer International Publishing Switzerland
eBook ISBN
978-3-319-13467-3
DOI
10.1007/978-3-319-13467-3
Hardcover ISBN
978-3-319-13466-6
Softcover ISBN
978-3-319-37433-8
Buchreihen ISSN
0072-5285
Auflage
2
Seitenzahl
XIII, 453
Anzahl der Bilder und Tabellen
7 schwarz-weiß Abbildungen, 72 Abbildungen in Farbe
Themen