Semisolvability of semisimple Hopf algebras of low dimension:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
2007
|
| Series: | Memoirs of the American Mathematical Society
874 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 186, number 874 (fourth of five numbers.)" Includes bibliographical references E |
| Physical Description: | VII, 123 S. |
| ISBN: | 0821839489 9780821839485 |
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MARC
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| 245 | 1 | 0 | |a Semisolvability of semisimple Hopf algebras of low dimension |c Sonia Natale |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2007 | |
| 300 | |a VII, 123 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v 874 | |
| 500 | |a "Volume 186, number 874 (fourth of five numbers.)" | ||
| 500 | |a Includes bibliographical references | ||
| 500 | |a E | ||
| 650 | 7 | |a Anéis de grupos |2 larpcal | |
| 650 | 7 | |a Grupos quânticos |2 larpcal | |
| 650 | 7 | |a Hopf-algebra's |2 gtt | |
| 650 | 7 | |a Kwantumgroepen |2 gtt | |
| 650 | 4 | |a Hopf algebras | |
| 650 | 4 | |a Quantum groups | |
| 650 | 0 | 7 | |a Hopf-Algebra |0 (DE-588)4160646-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantengruppe |0 (DE-588)4252437-4 |2 gnd |9 rswk-swf |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction and Main Results 1
Conventions and Notation. 7
Chapter 1. Semisimple Hopf Algebras 9
1.1. Algebra structure 9
1.2. Irreducible characters 10
1.3. Coinvariants of Hopf algebra maps 12
1.4. Yetter Drinfeld modules 13
1.5. Yetter Drinfeld modules and the character algebra 14
1.6. One dimensional Yetter Drinfeld modules 15
1.7. HcoB as a left coideal of H 16
Chapter 2. The Nichols Richmond Theorem 17
2.1. Irreducible characters of degree 2 17
2.2. The Nichols Richmond theorem 19
2.3. An application to D(H) 20
2.4. Existence of proper Hopf subalgebras 20
2.5. Hopf subalgebras of index 3 22
Chapter 3. Quotient Coalgebras 25
3.1. A multiplicity formula 25
3.2. Stable subcoalgebras 27
3.3. Quotients modulo group like Hopf subalgebras 30
3.4. On the structure of G(H) 31
3.5. A criterion of normality 32
Chapter 4. Braided Hopf Algebras 33
4.1. Radford Majid biproduct construction 33
4.2. Coalgebra structure of R 34
4.3. Hopf subalgebras 36
4.4. Biproducts over finite groups 37
4.5. Cocommutative braided Hopf algebras 39
4.6. Cocommutative braided Hopf algebras over Zp 40
4.7. Transitive actions of central subgroups 43
V
vi CONTENTS
Chapter 5. Cocycle Deformations of Some Hopf Algebras 45
5.1. Lifting from abelian groups 45
5.2. Examples in dimension pq2; p = 1 mod q 46
5.3. Examples in dimension pq2; q = 1 mod p 47
5.4. Normal Hopf subalgebras in cocycle twists 47
Chapter 6. Dimension 24 49
6.1. Possible (co) algebra structures 49
6.2. Upper and lower semisolvability 54
Chapter 7. Dimension 30 57
7.1. Possible (co) algebra structures 57
7.2. Classification 60
Chapter 8. Dimension 36 61
8.1. Reduction of the problem 61
8.2. Main result 67
Chapter 9. Dimension 40 69
9.1. Reduction of the problem 69
9.2. Main result 73
Chapter 10. Dimension 42 75
10.1. Possible (co) algebra structures 75
10.2. Classification 79
Chapter 11. Dimension 48 81
11.1. First reduction 81
11.2. Further reductions 92
11.3. Main result up to cocycle twists 96
11.4. Main result 101
Chapter 12. Dimension 54 107
12.1. First reduction 107
12.2. Main result 111
Chapter 13. Dimension 56 113
13.1. First reduction 113
13.2. Main result 115
Appendix A. Drinfeld Double of H8 117
A.I. Structure of D(H8) 117
A.2. Proof of Theorem A. 1.1 118
A.3. Proof of Theorem A. 1.2 120
Appendix. Bibliography 121
|
| adam_txt |
Contents
Introduction and Main Results 1
Conventions and Notation. 7
Chapter 1. Semisimple Hopf Algebras 9
1.1. Algebra structure 9
1.2. Irreducible characters 10
1.3. Coinvariants of Hopf algebra maps 12
1.4. Yetter Drinfeld modules 13
1.5. Yetter Drinfeld modules and the character algebra 14
1.6. One dimensional Yetter Drinfeld modules 15
1.7. HcoB as a left coideal of H 16
Chapter 2. The Nichols Richmond Theorem 17
2.1. Irreducible characters of degree 2 17
2.2. The Nichols Richmond theorem 19
2.3. An application to D(H) 20
2.4. Existence of proper Hopf subalgebras 20
2.5. Hopf subalgebras of index 3 22
Chapter 3. Quotient Coalgebras 25
3.1. A multiplicity formula 25
3.2. Stable subcoalgebras 27
3.3. Quotients modulo group like Hopf subalgebras 30
3.4. On the structure of G(H) 31
3.5. A criterion of normality 32
Chapter 4. Braided Hopf Algebras 33
4.1. Radford Majid biproduct construction 33
4.2. Coalgebra structure of R 34
4.3. Hopf subalgebras 36
4.4. Biproducts over finite groups 37
4.5. Cocommutative braided Hopf algebras 39
4.6. Cocommutative braided Hopf algebras over Zp 40
4.7. Transitive actions of central subgroups 43
V
vi CONTENTS
Chapter 5. Cocycle Deformations of Some Hopf Algebras 45
5.1. Lifting from abelian groups 45
5.2. Examples in dimension pq2; p = 1 mod q 46
5.3. Examples in dimension pq2; q = 1 mod p 47
5.4. Normal Hopf subalgebras in cocycle twists 47
Chapter 6. Dimension 24 49
6.1. Possible (co) algebra structures 49
6.2. Upper and lower semisolvability 54
Chapter 7. Dimension 30 57
7.1. Possible (co) algebra structures 57
7.2. Classification 60
Chapter 8. Dimension 36 61
8.1. Reduction of the problem 61
8.2. Main result 67
Chapter 9. Dimension 40 69
9.1. Reduction of the problem 69
9.2. Main result 73
Chapter 10. Dimension 42 75
10.1. Possible (co) algebra structures 75
10.2. Classification 79
Chapter 11. Dimension 48 81
11.1. First reduction 81
11.2. Further reductions 92
11.3. Main result up to cocycle twists 96
11.4. Main result 101
Chapter 12. Dimension 54 107
12.1. First reduction 107
12.2. Main result 111
Chapter 13. Dimension 56 113
13.1. First reduction 113
13.2. Main result 115
Appendix A. Drinfeld Double of H8 117
A.I. Structure of D(H8) 117
A.2. Proof of Theorem A. 1.1 118
A.3. Proof of Theorem A. 1.2 120
Appendix. Bibliography 121 |
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| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T17:04:47Z |
| indexdate | 2024-07-09T20:56:02Z |
| institution | BVB |
| isbn | 0821839489 9780821839485 |
| language | English |
| lccn | 2006047928 |
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| physical | VII, 123 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
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| publisher | American Mathematical Society |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Natale, Sonia 1972- Verfasser (DE-588)173905897 aut Semisolvability of semisimple Hopf algebras of low dimension Sonia Natale Providence, RI American Mathematical Society 2007 VII, 123 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 874 "Volume 186, number 874 (fourth of five numbers.)" Includes bibliographical references E Anéis de grupos larpcal Grupos quânticos larpcal Hopf-algebra's gtt Kwantumgroepen gtt Hopf algebras Quantum groups Hopf-Algebra (DE-588)4160646-2 gnd rswk-swf Quantengruppe (DE-588)4252437-4 gnd rswk-swf Hopf-Algebra (DE-588)4160646-2 s Quantengruppe (DE-588)4252437-4 s DE-604 Memoirs of the American Mathematical Society 874 (DE-604)BV008000141 874 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015574084&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Natale, Sonia 1972- Semisolvability of semisimple Hopf algebras of low dimension Memoirs of the American Mathematical Society Anéis de grupos larpcal Grupos quânticos larpcal Hopf-algebra's gtt Kwantumgroepen gtt Hopf algebras Quantum groups Hopf-Algebra (DE-588)4160646-2 gnd Quantengruppe (DE-588)4252437-4 gnd |
| subject_GND | (DE-588)4160646-2 (DE-588)4252437-4 |
| title | Semisolvability of semisimple Hopf algebras of low dimension |
| title_auth | Semisolvability of semisimple Hopf algebras of low dimension |
| title_exact_search | Semisolvability of semisimple Hopf algebras of low dimension |
| title_exact_search_txtP | Semisolvability of semisimple Hopf algebras of low dimension |
| title_full | Semisolvability of semisimple Hopf algebras of low dimension Sonia Natale |
| title_fullStr | Semisolvability of semisimple Hopf algebras of low dimension Sonia Natale |
| title_full_unstemmed | Semisolvability of semisimple Hopf algebras of low dimension Sonia Natale |
| title_short | Semisolvability of semisimple Hopf algebras of low dimension |
| title_sort | semisolvability of semisimple hopf algebras of low dimension |
| topic | Anéis de grupos larpcal Grupos quânticos larpcal Hopf-algebra's gtt Kwantumgroepen gtt Hopf algebras Quantum groups Hopf-Algebra (DE-588)4160646-2 gnd Quantengruppe (DE-588)4252437-4 gnd |
| topic_facet | Anéis de grupos Grupos quânticos Hopf-algebra's Kwantumgroepen Hopf algebras Quantum groups Hopf-Algebra Quantengruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015574084&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT natalesonia semisolvabilityofsemisimplehopfalgebrasoflowdimension |