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Book: An Elementary Introduction to Groups and Representations
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An Elementary Introduction to Groups and Representations
Authors: Brian C. Hall, University of Notre Dame, Department of Mathematics, Notre Dame, USA
Uploaded by:
bci1
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- Comments:
- 128 pages, year 2000 PDf at arxiv
- Abstract:
- Book Contents:
1. Preface v
Chapter 1. Groups 1
1. Definition of a Group, and Basic Properties 1
2. Some Examples of Groups 3
3. Subgroups, the Center, and Direct Products 4
4. Homomorphisms and Isomorphisms 5
5. Exercises 6
Chapter 2. Matrix Lie Groups 9
1. Definition of a Matrix Lie Group 9
2. Examples of Matrix Lie Groups 10
3. Compactness 15
4. Connectedness 16
5. Simple-connectedness 18
6. Homomorphisms and Isomorphisms 19
7. Lie Groups 20
8. Exercises 22
Chapter 3. Lie Algebras and the Exponential Mapping 27
1. The Matrix Exponential 27
2. Computing the Exponential of a Matrix 29
3. The Matrix Logarithm 31
4. Further Properties of the Matrix Exponential 34
5. The Lie Algebra of a Matrix Lie Group 36
6. Properties of the Lie Algebra 40
7. The Exponential Mapping 44
8. Lie Algebras 46
9. The Complexification of a Real Lie Algebra 48
10. Exercises 50
Chapter 4. The Baker-Campbell-Hausdorff Formula 53
1. The Baker-Campbell-Hausdorff Formula for the Heisenberg Group 53
2. The General Baker-Campbell-Hausdorff Formula 56
3. The Series Form of the Baker-Campbell-Hausdorff Formula 63
4. Subgroups and Subalgebras 64
5. Exercises 65
Chapter 5. Basic Representation Theory 67
1. Representations 67
2. Why Study Representations? 69
iii
http://www.mrao.cam.ac.uk/~clifford/ptIIIcourse/course99/
- Rights:
-
Open access, free online downloads of PDF file at;
http://www.mrao.cam.ac.uk/~clifford/ptIIIcourse/course99/
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Pending Errata and Addenda
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