Lie groups, Lie algebras, and representations : an elementary introduction / Brian Hall.

By:

Hall, Brian

Series: Graduate texts in mathematics ; 222Publication details: Switzerland : Springer, 2015.Edition: 2nd edDescription: xiii, 449 p. : illustrations ; 25 cmISBN:

9783319134666

Subject(s):

DDC classification:

512.55 23 H174

Contents:

Part I: General Theory.- 1. Matrix Lie Groups -- 2. The Matrix Exponential -- 3. Lie Algebras -- 4. Basic Representation Theory -- 5. The Baker?Campbell?Hausdorff Formula and its Consequences -- Part II: Semisimple Lie Algebras -- 6. The Representations of sl(3;C).- 7. Semisimple Lie Algebras.- 8. Root Systems -- 9. Representations of Semisimple Lie Algebras -- 10. Further Properties of the Representations -- Part III: Compact lie Groups -- 11. Compact Lie Groups and Maximal Tori -- 12. The Compact Group Approach to Representation Theory -- 13. Fundamental Groups of Compact Lie Groups -- A. Linear algebra review-- B. Differential forms-- C. Clebsch-Gordan theory and the Wigner-Eckart theorem-- D. Completeness of characters-- References-- Index.

Summary: This book 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.

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Item type	Current library	Call number	Status	Date due	Barcode	Item holds
Books	ISI Library, Kolkata	512.55 H174 (Browse shelf(Opens below))	Available		136485

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Previous	512.55 H148 Classical groups and K-theory	512.55 H174 Lie groups, Lie algebras, and representations an elementary introduction	512.55 H174 Lie groups, Lie algebras, and representations an elementary introduction	512.55 H174 Lie groups, Lie algebras, and representations : an elementary introduction /	512.55 H282 Automorphic forms on semisimple lie groups	512.55 H282 Representations of semisimple lie groups 4. 1955	512.55 H293 Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space	Next

Includes bibliographical references and index.

Part I: General Theory.-
1. Matrix Lie Groups --
2. The Matrix Exponential --
3. Lie Algebras --
4. Basic Representation Theory --
5. The Baker?Campbell?Hausdorff Formula and its Consequences --

Part II: Semisimple Lie Algebras --
6. The Representations of sl(3;C).-
7. Semisimple Lie Algebras.-
8. Root Systems --
9. Representations of Semisimple Lie Algebras --
10. Further Properties of the Representations --

Part III: Compact lie Groups --
11. Compact Lie Groups and Maximal Tori --
12. The Compact Group Approach to Representation Theory --
13. Fundamental Groups of Compact Lie Groups --
A. Linear algebra review--
B. Differential forms--
C. Clebsch-Gordan theory and the Wigner-Eckart theorem--
D. Completeness of characters--
References--
Index.

This book 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.

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