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

By: Hall, Brian.
Series: Graduate texts in mathematics ; 222.Publisher: Switzerland : Springer, 2015Edition: 2nd ed.Description: xiii, 449 p. : illustrations ; 25 cm.ISBN: 9783319134666.Subject(s): Lie groups | Lie algebrasDDC classification: 512.55
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 location Call number Status Date due Barcode Item holds
Books Books ISI Library, Kolkata
 
512.55 H174 (Browse shelf) Available 136485
Total holds: 0

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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