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: 512.55Item type  Current location  Call number  Status  Date due  Barcode  Item holds  

Books 
ISI Library, Kolkata

512.55 H174 (Browse shelf)  Available  136485 
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. ClebschGordan theory and the WignerEckart 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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