Blocks and families for cyclotomic Hecke algebras:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
2009
|
| Series: | Lecture notes in mathematics
1981 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 160 S. 235 mm x 155 mm |
| ISBN: | 9783642030635 |
Staff View
MARC
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| 100 | 1 | |a Chlouveraki, Maria |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Blocks and families for cyclotomic Hecke algebras |c Maria Chlouveraki |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c 2009 | |
| 300 | |a XIII, 160 S. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1981 | |
| 502 | |a Zugl.: Paris, Univ., Diss., 2007 u.d.T.: Chlouveraki, Maria: On the cyclotomic Hecke algebras of complex reflection GroupsGroups | ||
| 650 | 4 | |a Hecke-Algebra - Symmetrische Algebra - Spiegelungsgruppe - Charakter <Gruppentheorie> - Block <Mathematik> | |
| 650 | 4 | |a Cyclotomy | |
| 650 | 4 | |a Hecke algebras | |
| 650 | 4 | |a Representations of groups | |
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| 650 | 0 | 7 | |a Block |g Mathematik |0 (DE-588)4146017-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Spiegelungsgruppe |0 (DE-588)4182257-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hecke-Algebra |0 (DE-588)4159341-8 |2 gnd |9 rswk-swf |
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| 689 | 0 | 4 | |a Block |g Mathematik |0 (DE-588)4146017-0 |D s |
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Record in the Search Index
| _version_ | 1804140716773867520 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
1 ON COMMUTATIVE ALGEBRA 1
1.1 LOCALIZATIONS 1
1.2 INTEGRALI}- CLOSED RINGS 3
1.2.1 LIFTING PRIME IDEALS 4
1.2.2 VALUATIONS 5
1.2.3 DISCRETE VALUATION RINGS AND KRULL RINGS 8
1.3 COMPLETIONS 9
1.4 MORPHISMS ASSOCIATED WITH MONOMIALS AND ADAPTED MORPHISMS 10
1.5 IRREDUCIBILITY 16
2 ON BLOCKS 21
2.1 GENERAL RESULTS 21
2.1.1 BLOCKS AND INTEGRAL CLOSURE 25
2.1.2 BLOCKS AND PRIME IDEALS 27
2.1.3 BLOCKS AND QUOTIENT BLOCKS 28
2.1.4 BLOCKS AND CENTRAL CHARACTERS 30
2.2 SYMMETRIC ALGEBRAS 30
2.3 TWISTED SYMMETRIC ALGEBRAS OF FINITE GROUPS 33
2.3.1 ACTION OF G ON ZAE 38
2.3.2 MULTIPLICATION OF AN ^-MODULE BY AN OG- MODULE 40 2.3.3 INDUCTION
AND RESTRICTION OF AE J4-MODULES AND /^-MODULES 41
2.3.4 BLOCKS OF A AND BLOCKS OF A 40
2.4 REPRESENTATION THEORY OF SYMMETRIC ALGEBRAS 48
2.4.1 GROTHENDIECK GROUPS 48
2.4.2 INTEGRALITY 50
2.4.3 THE DECOMPOSITION MAP 52
2.4.4 A VARIATION FOR TITS DEFORMATION THEOREM 55
2.4.5 SYMMETRIC ALGEBRAS OVER DISCRETE VALUATION RINGS 56
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/994680414
DIGITALISIERT DURCH
IMAGE 2
XII CONTENTS
3 ON ESSENTIAL ALGEBRAS 61
3.1 GENERAL FACTS 61
3.2 SPECIALIZATION VIA MORPHISMS ASSOCIATED WITH MONOMIALS 63 3.3
SPECIALIZATION VIA ADAPTED MORPHISMS 66
3.4 THE MAP I N 69
4 ON HECKE ALGEBRAS 71
4.1 COMPLEX REFLECTION GROUPS AND ASSOCIATED BRAID GROUPS 71 4.1.1
COMPLEX REFLECTION GROUPS 72
4.1.2 BRAID GROUPS ASSOCIATED TO COMPLEX REFLECTION GROUPS 72 4.2
GENERIC HECKE ALGEBRAS 75
4.3 CYCLOTOMIC HECKE ALGEBRAS 80
4.3.1 ESSENTIAL HYPERPLANES 82
4.3.2 GROUP ALGEBRA 83
4.4 ROUQUIER BLOCKS OF THE CYCLOTOMIC HECKE ALGEBRAS 84
4.4.1 ROUQUIER BLOCKS AND CENTRAL MORPHISMS 87
4.4.2 ROUQUIER BLOCKS AND FUNCTIONS A AND A 87
5 ON THE DETERMINATION OF THE ROUQUIER BLOCKS 91
5.1 GENERAL PRINCIPLES 92
5.2 THE EXCEPTIONAL IRREDUCIBLE COMPLEX REFLECTION GROUPS 94 5.2.1
ESSENTIAL HYPERPLANES 94
5.2.2 ALGORITHM 96
5.2.3 RESULTS 97
5.3 THE GROUPS G(D, 1, R) 104
5.3.1 COMBINATORICS 104
5.3.2 ARIKI-KOIKE ALGEBRAS 107
5.3.3 ROUQUIER BLOCKS, CHARGED CONTENT AND RESIDUES 108 5.3.4 ESSENTIAL
HYPERPLANES 110
5.3.5 RESULTS 110
5.4 THE GROUPS G(2D, 2,2) 117
5.4.1 ESSENTIAL HYPERPLANES 117
5.4.2 RESULTS 118
5.5 THE GROUPS G(DE, E,R) 122
5.5.1 THE GROUPS G(DE,E,R), R 2 122
5.5.2 THE GROUPS G(DE,E, 2) 128
A CLIFFORD THEORY AND SCHUR ELEMENTS FOR GENERIC HECKE ALGEBRAS 133
A.I THE GROUPS G 4 , G S , G 6 , G 7 133
A.2 THE GROUPS G 8 , G 9 , G 10 , G N , G I2 , G I3 , GN, G I5 136
A.3 THE GROUPS GI 6 , G L7 , GI 8 , G I9 , G 20 , G 2U G 22 I 40 A.4 THE
GROUPS G 25 , G 2 E 1 44
A.5 THE GROUP G 2S C W) 1 46
A.6 THE GROUP G32 1 47
IMAGE 3
CONTENTS X
A.7 THE GROUPS G (DE, E, R) 150
A.7.1 THE GROUPS G(DE, E, R), R 2 150
A.7.2 THEGROUPSG((IE,E,2), E ODD 152
A.7.3 THE GROUPS G(DE, E, 2), E EVEN 152
REFERENCES 155
INDEX 159
|
| any_adam_object | 1 |
| author | Chlouveraki, Maria |
| author_facet | Chlouveraki, Maria |
| author_role | aut |
| author_sort | Chlouveraki, Maria |
| author_variant | m c mc |
| building | Verbundindex |
| bvnumber | BV035781294 |
| callnumber-first | Q - Science |
| callnumber-label | QA176 |
| callnumber-raw | QA176 QA3 |
| callnumber-search | QA176 QA3 |
| callnumber-sort | QA 3176 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| classification_tum | MAT 202f |
| ctrlnum | (OCoLC)428028860 (DE-599)DNB994680414 |
| dewey-full | 512.2222 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2222 |
| dewey-search | 512.2222 |
| dewey-sort | 3512.2222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| id | DE-604.BV035781294 |
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| indexdate | 2024-07-09T22:04:24Z |
| institution | BVB |
| isbn | 9783642030635 |
| language | English |
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| physical | XIII, 160 S. 235 mm x 155 mm |
| publishDate | 2009 |
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| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Chlouveraki, Maria Verfasser aut Blocks and families for cyclotomic Hecke algebras Maria Chlouveraki Berlin ; Heidelberg Springer 2009 XIII, 160 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1981 Zugl.: Paris, Univ., Diss., 2007 u.d.T.: Chlouveraki, Maria: On the cyclotomic Hecke algebras of complex reflection GroupsGroups Hecke-Algebra - Symmetrische Algebra - Spiegelungsgruppe - Charakter <Gruppentheorie> - Block <Mathematik> Cyclotomy Hecke algebras Representations of groups Charakter Gruppentheorie (DE-588)4158438-7 gnd rswk-swf Symmetrische Algebra (DE-588)4373936-2 gnd rswk-swf Block Mathematik (DE-588)4146017-0 gnd rswk-swf Spiegelungsgruppe (DE-588)4182257-2 gnd rswk-swf Hecke-Algebra (DE-588)4159341-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Hecke-Algebra (DE-588)4159341-8 s Symmetrische Algebra (DE-588)4373936-2 s Spiegelungsgruppe (DE-588)4182257-2 s Charakter Gruppentheorie (DE-588)4158438-7 s Block Mathematik (DE-588)4146017-0 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-03064-2 Lecture notes in mathematics 1981 (DE-604)BV000676446 1981 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018640803&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chlouveraki, Maria Blocks and families for cyclotomic Hecke algebras Lecture notes in mathematics Hecke-Algebra - Symmetrische Algebra - Spiegelungsgruppe - Charakter <Gruppentheorie> - Block <Mathematik> Cyclotomy Hecke algebras Representations of groups Charakter Gruppentheorie (DE-588)4158438-7 gnd Symmetrische Algebra (DE-588)4373936-2 gnd Block Mathematik (DE-588)4146017-0 gnd Spiegelungsgruppe (DE-588)4182257-2 gnd Hecke-Algebra (DE-588)4159341-8 gnd |
| subject_GND | (DE-588)4158438-7 (DE-588)4373936-2 (DE-588)4146017-0 (DE-588)4182257-2 (DE-588)4159341-8 (DE-588)4113937-9 |
| title | Blocks and families for cyclotomic Hecke algebras |
| title_auth | Blocks and families for cyclotomic Hecke algebras |
| title_exact_search | Blocks and families for cyclotomic Hecke algebras |
| title_full | Blocks and families for cyclotomic Hecke algebras Maria Chlouveraki |
| title_fullStr | Blocks and families for cyclotomic Hecke algebras Maria Chlouveraki |
| title_full_unstemmed | Blocks and families for cyclotomic Hecke algebras Maria Chlouveraki |
| title_short | Blocks and families for cyclotomic Hecke algebras |
| title_sort | blocks and families for cyclotomic hecke algebras |
| topic | Hecke-Algebra - Symmetrische Algebra - Spiegelungsgruppe - Charakter <Gruppentheorie> - Block <Mathematik> Cyclotomy Hecke algebras Representations of groups Charakter Gruppentheorie (DE-588)4158438-7 gnd Symmetrische Algebra (DE-588)4373936-2 gnd Block Mathematik (DE-588)4146017-0 gnd Spiegelungsgruppe (DE-588)4182257-2 gnd Hecke-Algebra (DE-588)4159341-8 gnd |
| topic_facet | Hecke-Algebra - Symmetrische Algebra - Spiegelungsgruppe - Charakter <Gruppentheorie> - Block <Mathematik> Cyclotomy Hecke algebras Representations of groups Charakter Gruppentheorie Symmetrische Algebra Block Mathematik Spiegelungsgruppe Hecke-Algebra Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018640803&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT chlouverakimaria blocksandfamiliesforcyclotomicheckealgebras |