Principal structures and methods of representation theory:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, RI
American Mathematical Society
2006
|
| Series: | Translations of mathematical monographs
228 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 430 S. graph. Darst. |
| ISBN: | 0821837311 |
Staff View
MARC
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| 240 | 1 | 0 | |a Osnovnye struktury i metody teorii predstavlenij |
| 245 | 1 | 0 | |a Principal structures and methods of representation theory |c D. Zhelobenko |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2006 | |
| 300 | |a XI, 430 S. |b graph. Darst. | ||
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Record in the Search Index
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| adam_text | Contents
Preface ix
Part 1. Introduction 1
Chapter 1. Basic Notions 3
1. Algebraic structures 3
2. Vector spaces 8
3. Elements of linear algebra 14
4. Functional calculus 20
5. Unitary spaces 26
6. Tensor products 35
7. S modules 40
Comments to Chapter 1 46
Part 2. General Theory 49
Chapter 2. Associative Algebras 51
8. Algebras and modules 51
9. Semisimple modules 58
10. Group algebras 64
11. Systems of generators 70
12. Tensor algebras 75
13. Formal series 80
14. Weyl algebras 86
15. Elements of ring theory 93
Comments to Chapter 2 98
Chapter 3. Lie Algebras 99
16. General questions 99
17. Solvable Lie algebras 105
18. Bilinear forms 109
19. The algebra U{g) 115
20. Semisimple Lie algebras 120
21. Free Lie algebras 125
22. Examples of Lie algebras 130
Comments to Chapter 3 137
Chapter 4. Topological Groups 139
23. Topological groups 139
24. Topological vector spaces 145
V
vi CONTENTS
25. Topological modules 152
26. Invariant measures 157
27. Group algebras 164
28. Compact groups 170
29. Solvable groups 175
30. Algebraic groups 181
Comments to Chapter 4 185
Chapter 5. Lie Groups 187
31. Manifolds 187
32. Lie groups 192
33. Formal groups 198
34. Local Lie groups 203
35. Connected Lie groups 209
36. Representations of Lie groups 214
37. Examples and exercises 219
Comments to Chapter 5 224
Part 3. Special Topics 225
Chapter 6. Semisimple Lie Algebras 227
38. Cartan subalgebras 227
39. Classification 233
40. Verma modules 238
41. Finite dimensional g modules 244
42. The algebra Z{g) 250
43. The algebra Fext(g) 256
Comments to Chapter 6 262
Chapter 7. Semisimple Lie Groups 263
44. Reductive Lie groups 263
45. Compact Lie groups 268
46. Maximal tori 272
47. Semisimple Lie groups 277
48. The algebra A(G) 283
49. The classical groups 289
50. Reduction problems 294
Comments to Chapter 7 300
Chapter 8. Banach Algebras 301
51. Banach algebras 301
52. The commutative case 307
53. Spectral theory 312
54. C algebras 317
55. Representations of C* algebras 323
56. Von Neumann algebras 329
57. The algebra C*{G) 335
58. Abelian groups 340
Comments to Chapter 8 346
CONTENTS vii
Chapter 9. Quantum Groups 347
59. Hopf algebras 347
60. Weyl algebras 353
61. The algebra Uq(g) 359
62. The category Oint 365
63. The algebra Aq(g) 370
64. Gaussian algebras 377
65. Projective limits 383
Comments to Chapter 9 388
Appendix A. Root Systems 391
Comments to Appendix A 402
Appendix B. Banach Spaces 403
Appendix C. Convex Sets 407
Appendix D. The Algebra B(H) 413
Bibliography 421
Index 425
|
| adam_txt |
Contents
Preface ix
Part 1. Introduction 1
Chapter 1. Basic Notions 3
1. Algebraic structures 3
2. Vector spaces 8
3. Elements of linear algebra 14
4. Functional calculus 20
5. Unitary spaces 26
6. Tensor products 35
7. S modules 40
Comments to Chapter 1 46
Part 2. General Theory 49
Chapter 2. Associative Algebras 51
8. Algebras and modules 51
9. Semisimple modules 58
10. Group algebras 64
11. Systems of generators 70
12. Tensor algebras 75
13. Formal series 80
14. Weyl algebras 86
15. Elements of ring theory 93
Comments to Chapter 2 98
Chapter 3. Lie Algebras 99
16. General questions 99
17. Solvable Lie algebras 105
18. Bilinear forms 109
19. The algebra U{g) 115
20. Semisimple Lie algebras 120
21. Free Lie algebras 125
22. Examples of Lie algebras 130
Comments to Chapter 3 137
Chapter 4. Topological Groups 139
23. Topological groups 139
24. Topological vector spaces 145
V
vi CONTENTS
25. Topological modules 152
26. Invariant measures 157
27. Group algebras 164
28. Compact groups 170
29. Solvable groups 175
30. Algebraic groups 181
Comments to Chapter 4 185
Chapter 5. Lie Groups 187
31. Manifolds 187
32. Lie groups 192
33. Formal groups 198
34. Local Lie groups 203
35. Connected Lie groups 209
36. Representations of Lie groups 214
37. Examples and exercises 219
Comments to Chapter 5 224
Part 3. Special Topics 225
Chapter 6. Semisimple Lie Algebras 227
38. Cartan subalgebras 227
39. Classification 233
40. Verma modules 238
41. Finite dimensional g modules 244
42. The algebra Z{g) 250
43. The algebra Fext(g) 256
Comments to Chapter 6 262
Chapter 7. Semisimple Lie Groups 263
44. Reductive Lie groups 263
45. Compact Lie groups 268
46. Maximal tori 272
47. Semisimple Lie groups 277
48. The algebra A(G) 283
49. The classical groups 289
50. Reduction problems 294
Comments to Chapter 7 300
Chapter 8. Banach Algebras 301
51. Banach algebras 301
52. The commutative case 307
53. Spectral theory 312
54. C' algebras 317
55. Representations of C* algebras 323
56. Von Neumann algebras 329
57. The algebra C*{G) 335
58. Abelian groups 340
Comments to Chapter 8 346
CONTENTS vii
Chapter 9. Quantum Groups 347
59. Hopf algebras 347
60. Weyl algebras 353
61. The algebra Uq(g) 359
62. The category Oint 365
63. The algebra Aq(g) 370
64. Gaussian algebras 377
65. Projective limits 383
Comments to Chapter 9 388
Appendix A. Root Systems 391
Comments to Appendix A 402
Appendix B. Banach Spaces 403
Appendix C. Convex Sets 407
Appendix D. The Algebra B(H) 413
Bibliography 421
Index 425 |
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| language | English Russian |
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| spelling | Želobenko, Dmitrij P. Verfasser aut Osnovnye struktury i metody teorii predstavlenij Principal structures and methods of representation theory D. Zhelobenko Providence, RI American Mathematical Society 2006 XI, 430 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 228 Représentations d'algèbres ram Représentations de groupes ram Representations of groups Representations of algebras Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 s DE-604 Translations of mathematical monographs 228 (DE-604)BV000002394 228 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014777463&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Želobenko, Dmitrij P. Principal structures and methods of representation theory Translations of mathematical monographs Représentations d'algèbres ram Représentations de groupes ram Representations of groups Representations of algebras Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4148816-7 |
| title | Principal structures and methods of representation theory |
| title_alt | Osnovnye struktury i metody teorii predstavlenij |
| title_auth | Principal structures and methods of representation theory |
| title_exact_search | Principal structures and methods of representation theory |
| title_exact_search_txtP | Principal structures and methods of representation theory |
| title_full | Principal structures and methods of representation theory D. Zhelobenko |
| title_fullStr | Principal structures and methods of representation theory D. Zhelobenko |
| title_full_unstemmed | Principal structures and methods of representation theory D. Zhelobenko |
| title_short | Principal structures and methods of representation theory |
| title_sort | principal structures and methods of representation theory |
| topic | Représentations d'algèbres ram Représentations de groupes ram Representations of groups Representations of algebras Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | Représentations d'algèbres Représentations de groupes Representations of groups Representations of algebras Darstellungstheorie |
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