Modular invariant theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
|
| Series: | Encyclopaedia of mathematical sciences
139 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIII, 233 S. 240 mm x 160 mm |
| ISBN: | 9783642174032 3642174035 9783642174049 |
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MARC
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Record in the Search Index
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IMAGE 1
CONTENTS
1 FIRST STEPS 1
1.1 GROUPS ACTING ON VECTOR SPACES AND COORDINATE RINGS 2 1.1.1 V VERSUS
V* 4
1.2 CONSTRUCTING INVARIANTS 6
1.3 ON STRUCTURES AND FUNDAMENTAL QUESTIONS 7
1.4 BOUNDS FOR GENERATING SETS 7
1.5 ON THE STRUCTURE OF K[V] G : THE NON-MODULAR CASE 8
1.6 STRUCTURE OF K[V] G : MODULAR CASE 9
1.7 INVARIANT FRACTION FIELDS 10
1.8 VECTOR INVARIANTS 11
1.9 POLARIZATION AND RESTITUTION 11
1.10 THE ROLE OF THE CYCLIC GROUP C P IN CHARACTERISTIC P 16
1.11 C P REPRESENTED ON A 2 DIMENSIONAL VECTOR SPACE IN CHARACTERISTIC P
17
1.12 A FURTHER EXAMPLE: C P REPRESENTED ON 2 V2 IN CHARACTERISTIC P 20
1.13 THE VECTOR INVARIANTS OF V 2 23
2 ELEMENTS OF ALGEBRAIC GEOMETRY AND COMMUTATIVE ALGEBRA 25 2.1 THE
ZARISKI TOPOLOGY 25
2.2 THE TOPOLOGICAL SPACE SPEC(S) 27
2.3 NOETHERIAN RINGS 27
2.4 LOCALIZATION AND FIELDS OF FRACTIONS 29
2.5 INTEGRAL EXTENSIONS 29
2.6 HOMOGENEOUS SYSTEMS OF PARAMETERS 30
2.7 REGULAR SEQUENCES 31
2.8 COHEN-MACAULAY RINGS 32
2.9 THE HUBERT SERIES 34
2.10 GRADED NAKAYAMA LEMMA 35
2.11 HUBERT SYZYGY THEOREM 36
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1007904224
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
3 APPLICATIONS OF COMMUTATIVE ALGEBRA TO INVARIANT THEORY . 39 3.1
HOMOGENEOUS SYSTEMS OF PARAMETERS 40
3.2 SYMMETRIC FUNCTIONS 44
3.3 THE DICKSON INVARIANTS 45
3.4 UPPER TRIANGULAR INVARIANTS 46
3.5 NOETHER'S BOUND 46
3.6 REPRESENTATIONS OF MODULAR GROUPS AND NOETHER'S BOUND . . . 48 3.7
MOLIEN'S THEOREM 50
3.7.1 THE HUBERT SERIES OF THE REGULAR REPRESENTATION OF THE KLEIN GROUP
51
3.7.2 THE HILBERT SERIES OF THE REGULAR REPRESENTATION OF C\ . 53 3.8
RINGS OF INVARIANTS OF P-GROUPS ARE UNIQUE FACTORIZATION DOMAINS 54
3.9 WHEN THE FIXED POINT SUBSPACE IS LARGE 55
4 EXAMPLES 59
4.1 THE CYCLIC GROUP OF ORDER 2, THE REGULAR REPRESENTATION . . . 61
4.2 A DIAGONAL REPRESENTATION OF C2 62
4.3 FRACTION FIELDS OF INVARIANTS OF P-GROUPS 62
4.4 THE ALTERNATING GROUP 64
4.5 INVARIANTS OF PERMUTATION GROUPS 65
4.6 GOEBEL'S THEOREM 66
4.7 THE RING OF INVARIANTS OF THE REGULAR REPRESENTATION OF THE KLEIN
GROUP 69
4.8 THE RING OF INVARIANTS OF THE REGULAR REPRESENTATION OF C4 . . 72
4.9 A 2 DIMENSIONAL REPRESENTATION OF C3, P = 2 75
4.10 THE THREE DIMENSIONAL MODULAR REPRESENTATION OF C P 75
4.10.1 PRIOR KNOWLEDGE OF THE HILBERT SERIES 76
4.10.2 WITHOUT THE USE OF THE HILBERT SERIES 78
5 MONOMIAL ORDERINGS AND SAGBI BASES 83
5.1 SAGBI BASES 85
5.1.1 SYMMETRIC POLYNOMIALS 89
5.2 FINITE SAGBI BASES 91
5.3 SAGBI BASES FOR PERMUTATION REPRESENTATIONS 93
6 BLOCK BASES 99
6.1 A BLOCK BASIS FOR THE SYMMETRIC GROUP 101
6.2 BLOCK BASES FOR P-GROUPS 103
7 THE CYCLIC GROUP C P 105
7.1 REPRESENTATIONS OF C P IN CHARACTERISTIC P 105
7.2 THE CP-MODULE STRUCTURE OF [V N ] 110
7.2.1 SHARPS AND FLATS 110
7.3 THE CP-MODULE STRUCTURE OF [V] 113
IMAGE 3
CONTENTS XI
7.4 THE FIRST FUNDAMENTAL THEOREM FOR V2 115
7.4.1 DYCK PATHS AND MULTI-LINEAR INVARIANTS 117
7.4.2 PROOF OF LEMMA 7.4.3 122
7.5 INTEGRAL INVARIANTS 124
7.6 INVARIANT FRACTION FIELDS AND LOCALIZED INVARIANTS 130 7.7 NOETHER
NUMBER FOR C P 132
7.8 HILBERT FUNCTIONS 138
8 POLYNOMIAL INVARIANT RINGS 141
8.1 STONG'S EXAMPLE 147
8.2 A COUNTEREXAMPLE 148
8.3 IRREDUCIBLE MODULAR REFLECTION GROUPS 149
8.3.1 REFLECTION GROUPS 150
8.3.2 GROUPS GENERATED BY HOMOLOGIES OF ORDER GREATER THAN 2 151
8.3.3 GROUPS GENERATED BY TRANSVECTIONS 151
9 THE TRANSFER 153
9.1 THE TRANSFER FOR NAKAJIMA GROUPS 164
9.2 COHEN-MACAULAY INVARIANT RINGS OF P-GROUPS 170
9.3 DIFFERENTS IN MODULAR INVARIANT THEORY 173
9.3.1 CONSTRUCTION OF THE VARIOUS DIFFERENT IDEALS 174
10 INVARIANT RINGS VIA LOCALIZATION 179
11 RINGS OF INVARIANTS WHICH ARE HYPERSURFACES 185
12 SEPARATING INVARIANTS 191
12.1 RELATION BETWEEN K[^] G AND SEPARATING SUBALGEBRAS 195 12.2
POLYNOMIAL SEPARATING ALGEBRAS AND SERRE'S THEOREM 198 12.3 POLARIZATION
AND SEPARATING INVARIANTS 201
13 USING SAGBI BASES TO COMPUTE RINGS OF INVARIANTS 205
14 LADDERS 211
14.1 GROUP COHOMOLOGY 213
14.2 COHOMOLOGY AND INVARIANT THEORY 214
REFERENCES 223
INDEX 231 |
| any_adam_object | 1 |
| author | Campbell, Harold E. A. Eddy 1954- Wehlau, David L. 1960- |
| author_GND | (DE-588)14347877X (DE-588)143479423 |
| author_facet | Campbell, Harold E. A. Eddy 1954- Wehlau, David L. 1960- |
| author_role | aut aut |
| author_sort | Campbell, Harold E. A. Eddy 1954- |
| author_variant | h e a e c heae heaec d l w dl dlw |
| building | Verbundindex |
| bvnumber | BV037221814 |
| classification_rvk | SK 260 |
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| ctrlnum | (OCoLC)707089940 (DE-599)DNB1007904224 |
| dewey-full | 512.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.23 |
| dewey-search | 512.23 |
| dewey-sort | 3512.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| spelling | Campbell, Harold E. A. Eddy 1954- Verfasser (DE-588)14347877X aut Modular invariant theory H. E. A. Eddy Campbell ; David L. Wehlau Berlin [u.a.] Springer 2011 XIII, 233 S. 240 mm x 160 mm txt rdacontent n rdamedia nc rdacarrier Encyclopaedia of mathematical sciences 139 Encyclopaedia of mathematical sciences / Invariant theory and algebraic transformation groups 8 Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Invariantentheorie (DE-588)4162209-1 gnd rswk-swf Modulare Darstellung (DE-588)4311996-7 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 s Modulare Darstellung (DE-588)4311996-7 s Invariantentheorie (DE-588)4162209-1 s DE-604 Wehlau, David L. 1960- Verfasser (DE-588)143479423 aut Invariant theory and algebraic transformation groups Encyclopaedia of mathematical sciences 8 (DE-604)BV014336202 8 Encyclopaedia of mathematical sciences 139 (DE-604)BV024126459 139 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3554080&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021135677&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Campbell, Harold E. A. Eddy 1954- Wehlau, David L. 1960- Modular invariant theory Encyclopaedia of mathematical sciences Endliche Gruppe (DE-588)4014651-0 gnd Invariantentheorie (DE-588)4162209-1 gnd Modulare Darstellung (DE-588)4311996-7 gnd |
| subject_GND | (DE-588)4014651-0 (DE-588)4162209-1 (DE-588)4311996-7 |
| title | Modular invariant theory |
| title_auth | Modular invariant theory |
| title_exact_search | Modular invariant theory |
| title_full | Modular invariant theory H. E. A. Eddy Campbell ; David L. Wehlau |
| title_fullStr | Modular invariant theory H. E. A. Eddy Campbell ; David L. Wehlau |
| title_full_unstemmed | Modular invariant theory H. E. A. Eddy Campbell ; David L. Wehlau |
| title_short | Modular invariant theory |
| title_sort | modular invariant theory |
| topic | Endliche Gruppe (DE-588)4014651-0 gnd Invariantentheorie (DE-588)4162209-1 gnd Modulare Darstellung (DE-588)4311996-7 gnd |
| topic_facet | Endliche Gruppe Invariantentheorie Modulare Darstellung |
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| volume_link | (DE-604)BV014336202 (DE-604)BV024126459 |
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