Introduction to complex reflection groups and their braid groups:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
|
| Schriftenreihe: | Lecture notes in mathematics
1988 |
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=3423991&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018967629&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverz. S.133 - 135 |
| Umfang: | XI, 138 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9783642111747 |
Internformat
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| 100 | 1 | |a Broué, Michel |d 1946- |e Verfasser |0 (DE-588)113828853 |4 aut | |
| 245 | 1 | 0 | |a Introduction to complex reflection groups and their braid groups |c Michel Broué |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XI, 138 S. |b graph. Darst. |c 235 mm x 155 mm | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1988 | |
| 500 | |a Literaturverz. S.133 - 135 | ||
| 650 | 4 | |a Reflection groups | |
| 650 | 4 | |a Weyl groups | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 001z 2001 B 999-1988 |
|---|---|
| DE-BY-TUM_katkey | 1723307 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010226636 |
| _version_ | 1821934820620500993 |
| adam_text | CONTENTS 1 PRELIMINARIES 1 1.1 REFLECTIONS AND ROOTS 1 1.1.1 RANK ONE
ENDOMORPHISMS 1 1.1.2 PROJECTIONS, TRANSVECTIONS, REFLECTIONS 2 1.1.3
REFLECTIONS 2 1.1.4 COMMUTING REFLECTIONS 3 1.2 REFLECTION GROUPS 4
1.2.1 ORTHOGONAL DECOMPOSITION 5 1.2.2 THE SHEPHARD-TODD CLASSIFICATION
6 1.2.3 REFLECTING PAIRS 8 2 PREREQUISITES AND COMPLEMENTS IN
COMMUTATIVE ALGEBRA .. 11 2.1 FINITE RING EXTENSIONS 11 2.1.1 PROPERTIES
AND DEFINITIONS 11 2.1.2 SPECTRA AND FINITE EXTENSIONS 12 2.1.3 CASE OF
INTEGRALLY CLOSED RINGS 13 2.1.4 KRULL DIMENSION: FIRST DEFINITIONS 13
2.2 JACOBSON RINGS AND HUBERT S NULLSTELLENSATZ 15 2.2.1 ON MAXIMAL
IDEAL OF POLYNOMIAL ALGEBRAS 15 2.2.2 RADICALS AND JACOBSON RINGS,
APPLICATION TO ALGEBRAIC VARIETIES 19 2.3 GRADED ALGEBRAS AND MODULES 20
2.3.1 GRADED MODULES 20 2.3.2 ELEMENTARY CONSTRUCTIONS 21 2.3.3 KOSZUL
COMPLEX 22 2.3.4 GRADED ALGEBRAS AND MODULES 23 2.3.5 THE HILBERT-SERRE
THEOREM 23 2.3.6 NAKAYAMA S LEMMA 24 2.4 POLYNOMIAL ALGEBRAS AND
PARAMETERS SUBALGEBRAS 26 2.4.1 DEGREES AND JACOBIAN 26 2.4.2 SYSTEMS OF
PARAMETERS 28 2.4.3 THE CHEVALLEY THEOREM 31 BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/1000035875 DIGITALISIERT DURCH CONTENTS
POLYNOMIAL INVARIANTS OF FINITE LINEAR GROUPS 35 3.1 FINITE GROUPS
INVARIANTS 35 3.1.1 GENERALITIES 35 3.1.2 CASE OF HEIGHT ONE PRIMES 37
3.2 FINITE LINEAR GROUPS ON SYMMETRIC ALGEBRAS 38 3.2.1 RAMIFICATION AND
REFLECTING PAIRS 39 3.2.2 LINEAR CHARACTERS ASSOCIATED WITH REFLECTING
HYPERPLANES 40 3.3 COINVARIANT ALGEBRA AND HARMONIC POLYNOMIALS 44 3.3.1
THE COINVARIANT ALGEBRA 44 3.3.2 GALOIS TWISTING OF A REPRESENTATION 45
3.3.3 DIFFERENTIAL OPERATORS, HARMONIC POLYNOMIALS 46 3.4 GRADED
CHARACTERS AND APPLICATIONS 48 3.4.1 GRADED CHARACTERS OF GRADED
FEG-MODULES 49 3.4.2 ISOTYPIC COMPONENTS OF THE SYMMETRIC ALGEBRA 50
3.4.3 SOME NUMERICAL IDENTITIES 50 3.4.4 ISOTYPIC COMPONENTS ARE
COHEN-MACAULAY 52 3.4.5 COMPUTATIONS WITH POWER SERIES 52 3.4.6 A SIMPLE
EXAMPLE 55 FINITE REFLECTION GROUPS IN CHARACTERISTIC ZERO 57 4.1 THE
SHEPHARD-TODD/CHEVALLEY-SERRE THEOREM 57 4.2 STEINBERG THEOREM AND FIRST
APPLICATIONS 60 4.2.1 THE JACOBIAN AS A MONOMIAL 60 4.2.2 ACTION OF THE
NORMALIZER AND GENERALIZED DEGREES 60 4.2.3 STEINBERG THEOREM 62 4.2.4
FIXED POINTS OF ELEMENTS OF G 64 4.2.5 BRAID GROUPS 65 4.3 COINVARIANT
ALGEBRA AND HARMONIC POLYNOMIALS 67 4.3.1 ON THE COINVARIANT ALGEBRA 67
4.3.2 LINEAR CHARACTERS AND THEIR ASSOCIATED POLYNOMIALS.. 69 4.3.3 THE
HARMONIC ELEMENTS OF A REFLECTION GROU CONTENTS XI 5 EIGENSPACES AND
REGULAR ELEMENTS 97 5.1 EIGENSPACES 97 5.1.1 PIANZOLA-WEISS FORMULA 97
5.1.2 MAXIMAL EIGENSPACES: LEHRER-SPRINGER THEORY 99 5.2 REGULAR
ELEMENTS 104 5.2.1 FIRST PROPERTIES 104 5.2.2 EXPONENTS AND EIGENVALUES
OF REGULAR ELEMENTS 106 5.3 REGULAR BRAID AUTOMORPHISMS 112 5.3.1
LIFTING REGULAR AUTOMORPHISMS: CASE WHEN THE BASE POINT IS AN
EIGENVECTOR 112 5.3.2 LIFTING REGULAR AUTOMORPHISMS: GENERAL CASE 115
5.3.3 LIFTING SPRINGER THEORY 117 COXETER AND ARTIN-LIKE PRESENTATIONS
119 A COXETER AND ARTIN-LIKE PRESENTATIONS 119 A.I MEANING OF THE
DIAGRAMS 119 A.1.1 DIAGRAMS FOR THE REFLECTION GROUPS 119 A.1.2 BRAID
DIAGRAMS 121 A.2 TABLES 124 REFERENCES 133 INDEX 137
|
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| ctrlnum | (OCoLC)471803284 (DE-599)GBV620954884 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
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| dewey-search | 510 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV036076462 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T14:06:18Z |
| institution | BVB |
| isbn | 9783642111747 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018967629 |
| oclc_num | 471803284 |
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| physical | XI, 138 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spellingShingle | Broué, Michel 1946- Introduction to complex reflection groups and their braid groups Lecture notes in mathematics Reflection groups Weyl groups Zopfgruppe (DE-588)4225944-7 gnd Spiegelungsgruppe (DE-588)4182257-2 gnd |
| subject_GND | (DE-588)4225944-7 (DE-588)4182257-2 |
| title | Introduction to complex reflection groups and their braid groups |
| title_auth | Introduction to complex reflection groups and their braid groups |
| title_exact_search | Introduction to complex reflection groups and their braid groups |
| title_full | Introduction to complex reflection groups and their braid groups Michel Broué |
| title_fullStr | Introduction to complex reflection groups and their braid groups Michel Broué |
| title_full_unstemmed | Introduction to complex reflection groups and their braid groups Michel Broué |
| title_short | Introduction to complex reflection groups and their braid groups |
| title_sort | introduction to complex reflection groups and their braid groups |
| topic | Reflection groups Weyl groups Zopfgruppe (DE-588)4225944-7 gnd Spiegelungsgruppe (DE-588)4182257-2 gnd |
| topic_facet | Reflection groups Weyl groups Zopfgruppe Spiegelungsgruppe |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3423991&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018967629&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT brouemichel introductiontocomplexreflectiongroupsandtheirbraidgroups |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 001z 2001 B 999-1988
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |