Hopf algebras and their actions on rings:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
1993
|
| Schriftenreihe: | Regional Conference Series in Mathematics
82 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006482081&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIV, 238 Seiten |
| ISBN: | 0821807382 9780821807385 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV009797629 | ||
| 003 | DE-604 | ||
| 005 | 20210521 | ||
| 007 | t| | ||
| 008 | 940908s1993 xx |||| 10||| engod | ||
| 020 | |a 0821807382 |9 0-8218-0738-2 | ||
| 020 | |a 9780821807385 |9 978-0-8218-0738-5 | ||
| 035 | |a (OCoLC)605159828 | ||
| 035 | |a (DE-599)BVBBV009797629 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-739 |a DE-29T |a DE-384 |a DE-355 |a DE-19 |a DE-11 |a DE-188 |a DE-20 | ||
| 084 | |a SD 1992 |0 (DE-625)142726: |2 rvk | ||
| 084 | |a SI 195 |0 (DE-625)143098: |2 rvk | ||
| 084 | |a SK 230 |0 (DE-625)143225: |2 rvk | ||
| 100 | 1 | |a Montgomery, Susan |d 1943- |e Verfasser |0 (DE-588)1104783185 |4 aut | |
| 245 | 1 | 0 | |a Hopf algebras and their actions on rings |c Susan Montgomery |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 1993 | |
| 300 | |a XIV, 238 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Regional Conference Series in Mathematics |v 82 | |
| 650 | 0 | 7 | |a Assoziativer Ring |0 (DE-588)4143228-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Operation |g Mathematik |0 (DE-588)4115450-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hopf-Algebra |0 (DE-588)4160646-2 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Hopf-Algebra |0 (DE-588)4160646-2 |D s |
| 689 | 0 | 1 | |a Assoziativer Ring |0 (DE-588)4143228-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Hopf-Algebra |0 (DE-588)4160646-2 |D s |
| 689 | 1 | 1 | |a Operation |g Mathematik |0 (DE-588)4115450-2 |D s |
| 689 | 1 | 2 | |a Assoziativer Ring |0 (DE-588)4143228-9 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Regional Conference Series in Mathematics |v 82 |w (DE-604)BV000004346 |9 82 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006482081&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006482081 | |
Datensatz im Suchindex
| _version_ | 1819332544500334592 |
|---|---|
| adam_text | Contents
Preface xiii
Chapter 1. Definitions and Examples 1
1.1 Algebras and coalgebras 1
1.2 Duals of algebras and coalgebras 2
1.3 Bialgebras 3
1.4 Convolution and summation notation 6
1.5 Antipodes and Hopf algebras 7
1.6 Modules and comodules 10
1.7 Invariants and coinvariants 13
1.8 Tensor products of iJ modules and ^f comodules 14
1.9 Hopf modules 14
Chapter 2. Integrals and Semisimplicity 17
2.1 Integrals 17
2.2 Maschke s Theorem 20
2.3 Commutative semisimple Hopf algebras and restricted
enveloping algebras 22
2.4 Cosemisimplicity and integrals on H 25
2.5 Kaplansky s conjecture and the order of the antipode 27
Chapter 3. Freeness over Subalgebras 28
3.1 The Nichols Zoeller Theorem 28
3.2 Applications: Hopf algebras of prime dimension and semisimple
subHopfalgebras 31
3.3 A normal basis for H over K 32
3.4 The adjoint action, normal subHopfalgebras, and quotients 33
3.5 Freeness and faithful flatness in the infinite dimensional case 37
Chapter 4. Actions of Finite Dimensional Hopf Algebras and
Smash Products 40
4.1 Module algebras, comodule algebras, and smash products 40
4.2 Integrality and affine invariants: the commutative case 43
viii CONTENTS
4.3 Trace functions and affine invariants: the non commutative
case 45
4.4 Ideals in A#H and A as an A^ module 48
4.5 A Morita context relating A#H and AH 52
Chapter 5. Coradicals and Filtrations 56
5.1 Simple subcoalgebras and the coradical 56
5.2 The coradical nitration 60
5.3 Injective coalgebra maps 65
5.4 The coradical filtration of pointed coalgebras 67
5.5 Examples: U(g) and Uq(g) . 73
5.6 The structure of pointed cocommutative Hopf algebras 76
5.7 Semisimple cocommutative connected Hopf algebras 83
Chapter 6. Inner Actions 87
6.1 Definitions and examples 87
6.2 A Skolem Noether theorem for Hopf algebras 89
6.3 Maximal inner subcoalgebras 92
6.4 J^ inner actions and extending to quotients 96
Chapter 7. Crossed products 101
7.1 Definitions and examples 101
7.2 Cleft extensions and existence of crossed products 105
7.3 Inner actions and equivalence of crossed products 112
7.4 Generalized Maschke theorems and semiprime crossed
products 116
7.5 Twisted ijT comodule algebras 121
Chapter 8. Galois Extensions 123
8.1 Definition and examples 123
8.2 The normal basis property and cleft extensions 128
8.3 Galois extensions for finite dimensional H 131
8.4 Normal bases and Hopf algebra quotients 139
8.5 Relative Hopf modules 144
CONTENTS ix
Chapter 9. Duality 149
9.1 H° 149
9.2 SubHopfalgebras of H° and density 153
9.3 Classical duality 159
9.4 Duality for actions 161
9.5 Duality for graded algebras 172
Chapter 10. New Constructions from Quantum Groups 178
10.1 Quasitriangular and almost cocommutative Hopf algebras 178
10.2 Coquasitriangular and almost commutative Hopf algebras 184
10.3 The Drinfeld double 187
10.4 Braided monoidal categories 197
10.5 Hopf algebras in categories; graded Hopf algebras 203
10.6 Biproducts and Yetter Drinfeld modules 207
Appendix. Some quantum groups 217
References 223
Index 235
|
| any_adam_object | 1 |
| author | Montgomery, Susan 1943- |
| author_GND | (DE-588)1104783185 |
| author_facet | Montgomery, Susan 1943- |
| author_role | aut |
| author_sort | Montgomery, Susan 1943- |
| author_variant | s m sm |
| building | Verbundindex |
| bvnumber | BV009797629 |
| classification_rvk | SD 1992 SI 195 SK 230 |
| ctrlnum | (OCoLC)605159828 (DE-599)BVBBV009797629 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01983nam a2200469 cb4500</leader><controlfield tag="001">BV009797629</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210521 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">940908s1993 xx |||| 10||| engod</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0821807382</subfield><subfield code="9">0-8218-0738-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821807385</subfield><subfield code="9">978-0-8218-0738-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)605159828</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV009797629</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SD 1992</subfield><subfield code="0">(DE-625)142726:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 195</subfield><subfield code="0">(DE-625)143098:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 230</subfield><subfield code="0">(DE-625)143225:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Montgomery, Susan</subfield><subfield code="d">1943-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1104783185</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Hopf algebras and their actions on rings</subfield><subfield code="c">Susan Montgomery</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">1993</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIV, 238 Seiten</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Regional Conference Series in Mathematics</subfield><subfield code="v">82</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Assoziativer Ring</subfield><subfield code="0">(DE-588)4143228-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Operation</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4115450-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Hopf-Algebra</subfield><subfield code="0">(DE-588)4160646-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)1071861417</subfield><subfield code="a">Konferenzschrift</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Hopf-Algebra</subfield><subfield code="0">(DE-588)4160646-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Assoziativer Ring</subfield><subfield code="0">(DE-588)4143228-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Hopf-Algebra</subfield><subfield code="0">(DE-588)4160646-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Operation</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4115450-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="2"><subfield code="a">Assoziativer Ring</subfield><subfield code="0">(DE-588)4143228-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Regional Conference Series in Mathematics</subfield><subfield code="v">82</subfield><subfield code="w">(DE-604)BV000004346</subfield><subfield code="9">82</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006482081&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-006482081</subfield></datafield></record></collection> |
| genre | (DE-588)1071861417 Konferenzschrift gnd-content |
| genre_facet | Konferenzschrift |
| id | DE-604.BV009797629 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T09:42:21Z |
| institution | BVB |
| isbn | 0821807382 9780821807385 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006482081 |
| oclc_num | 605159828 |
| open_access_boolean | |
| owner | DE-12 DE-739 DE-29T DE-384 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 DE-188 DE-20 |
| owner_facet | DE-12 DE-739 DE-29T DE-384 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 DE-188 DE-20 |
| physical | XIV, 238 Seiten |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Regional Conference Series in Mathematics |
| series2 | Regional Conference Series in Mathematics |
| spellingShingle | Montgomery, Susan 1943- Hopf algebras and their actions on rings Regional Conference Series in Mathematics Assoziativer Ring (DE-588)4143228-9 gnd Operation Mathematik (DE-588)4115450-2 gnd Hopf-Algebra (DE-588)4160646-2 gnd |
| subject_GND | (DE-588)4143228-9 (DE-588)4115450-2 (DE-588)4160646-2 (DE-588)1071861417 |
| title | Hopf algebras and their actions on rings |
| title_auth | Hopf algebras and their actions on rings |
| title_exact_search | Hopf algebras and their actions on rings |
| title_full | Hopf algebras and their actions on rings Susan Montgomery |
| title_fullStr | Hopf algebras and their actions on rings Susan Montgomery |
| title_full_unstemmed | Hopf algebras and their actions on rings Susan Montgomery |
| title_short | Hopf algebras and their actions on rings |
| title_sort | hopf algebras and their actions on rings |
| topic | Assoziativer Ring (DE-588)4143228-9 gnd Operation Mathematik (DE-588)4115450-2 gnd Hopf-Algebra (DE-588)4160646-2 gnd |
| topic_facet | Assoziativer Ring Operation Mathematik Hopf-Algebra Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006482081&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004346 |
| work_keys_str_mv | AT montgomerysusan hopfalgebrasandtheiractionsonrings |