Computational invariant theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Series: | Encyclopaedia of mathematical sciences
130 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 268 S. |
| ISBN: | 3540434763 |
Staff View
MARC
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| 245 | 1 | 0 | |a Computational invariant theory |c Harm Derksen ; Gregor Kemper |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
| 300 | |a X, 268 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Encyclopaedia of mathematical sciences |v 130 | |
| 490 | 1 | |a Encyclopaedia of mathematical sciences / Invariant theory and algebraic transformation groups |v 1 | |
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Record in the Search Index
| _version_ | 1804129182174674944 |
|---|---|
| adam_text | Introduction
.................................................. 1
1
Constructive
Ideal Theory
................................ 7
1.1
Ideals and
Gröbner
Bases
................................ 8
1.2
Elimination Ideals
...................................... 13
1.3
Syzygy Modules
........................................ 18
1.4
Hubert Series
.......................................... 22
1.5
The Radical Ideal
...................................... 27
1.6
Normalization
.......................................... 32
2
Invariant Theory
......................................... 39
2.1
Invariant Rings
......................................... 39
2.2
Reductive Groups
...................................... 44
2.3
Categorical Quotients
................................... 51
2.4
Homogeneous Systems of Parameters
..................... 59
2.5
The Cohen-Macaulay Property of Invariant Rings
.......... 62
2.6
Hubert Series of Invariant Rings
.......................... 69
3
Invariant Theory of Finite Groups
........................ 73
3.1
Homogeneous Components
.............................. 75
3.2
Molien s Formula
....................................... 76
3.3
Primary Invariants
..................................... 80
3.4
Cohen-Macaulayness
.................................... 86
3.5
Secondary Invariants
.................................... 89
3.6
Minimal Algebra Generators and Syzygies
................. 95
3.7
Properties of Invariant Rings
............................. 97
3.8
Noether s Degree Bound
.................................108
3.9
Degree Bounds in the Modular Case
......................112
3.10
Permutation Groups
....................................122
3.11
Ad Hoc Methods
.......................................130
4
Invariant Theory of Reductive Groups
....................139
4.1
Computing Invariants of Linearly Reductive Groups
........139
4.2
Improvements and Generalizations
........................150
4.3
Invariants of Tori
.......................................159
χ
Table of Contents
4.4
Invariants of SLn and GLn
..............................162
4.5
The Reynolds Operator
.................................166
4.6
Computing Hilbert Series
................................180
4.7
Degree Bounds for Invariants
............................196
4.8
Properties of Invariant Rings
.............................205
5
Applications of Invariant Theory
.........................209
5.1
Cohomology of Finite Groups
............................209
5.2
Galois Group Computation
..............................210
5.3
Noether s Problem and Generic Polynomials
...............215
5.4
Systems of Algebraic Equations with Symmetries
...........218
5.5
Graph Theory
.........................................220
5.6
Combinatorics
.........................................222
5.7
Coding Theory
.........................................224
5.8
Equivariant Dynamical Systems
..........................226
5.9
Material Science
........................................228
5.10
Computer Vision
.......................................231
A Linear Algebraic Groups
..................................237
A.I Linear Algebraic Groups
................................237
A.
2
The Lie Algebra of a Linear Algebraic Group
..............239
A.3 Reductive and Semi-simple Groups
.......................243
A.4 Roots
.................................................244
A.
5
Representation Theory
..................................245
References
....................................................247
Notation
......................................................261
Index
.........................................................263
|
| any_adam_object | 1 |
| author | Derksen, Harm 1970- Kemper, Gregor 1963- |
| author_GND | (DE-588)123662362 (DE-588)114214824 |
| author_facet | Derksen, Harm 1970- Kemper, Gregor 1963- |
| author_role | aut aut |
| author_sort | Derksen, Harm 1970- |
| author_variant | h d hd g k gk |
| building | Verbundindex |
| bvnumber | BV014289174 |
| classification_rvk | SK 260 |
| classification_tum | MAT 130f MAT 110f |
| ctrlnum | (OCoLC)248441667 (DE-599)BVBBV014289174 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014289174 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:01:04Z |
| institution | BVB |
| isbn | 3540434763 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009800374 |
| oclc_num | 248441667 |
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| owner_facet | DE-19 DE-BY-UBM DE-739 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-29T DE-634 DE-11 DE-188 |
| physical | X, 268 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series | Encyclopaedia of mathematical sciences |
| series2 | Encyclopaedia of mathematical sciences Encyclopaedia of mathematical sciences / Invariant theory and algebraic transformation groups |
| spelling | Derksen, Harm 1970- Verfasser (DE-588)123662362 aut Computational invariant theory Harm Derksen ; Gregor Kemper Berlin [u.a.] Springer 2002 X, 268 S. txt rdacontent n rdamedia nc rdacarrier Encyclopaedia of mathematical sciences 130 Encyclopaedia of mathematical sciences / Invariant theory and algebraic transformation groups 1 Kommutativer Ring - Invariantentheorie - Computeralgebra Computeralgebra (DE-588)4010449-7 gnd rswk-swf Invariantentheorie (DE-588)4162209-1 gnd rswk-swf Algebraische Transformationsgruppe (DE-588)4228484-3 gnd rswk-swf Kommutativer Ring (DE-588)4164825-0 gnd rswk-swf Algebraische Transformationsgruppe (DE-588)4228484-3 s Invariantentheorie (DE-588)4162209-1 s DE-604 Kommutativer Ring (DE-588)4164825-0 s Computeralgebra (DE-588)4010449-7 s Kemper, Gregor 1963- Verfasser (DE-588)114214824 aut Invariant theory and algebraic transformation groups Encyclopaedia of mathematical sciences 1 (DE-604)BV014336202 1 Encyclopaedia of mathematical sciences 130 (DE-604)BV024126459 130 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009800374&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Derksen, Harm 1970- Kemper, Gregor 1963- Computational invariant theory Encyclopaedia of mathematical sciences Kommutativer Ring - Invariantentheorie - Computeralgebra Computeralgebra (DE-588)4010449-7 gnd Invariantentheorie (DE-588)4162209-1 gnd Algebraische Transformationsgruppe (DE-588)4228484-3 gnd Kommutativer Ring (DE-588)4164825-0 gnd |
| subject_GND | (DE-588)4010449-7 (DE-588)4162209-1 (DE-588)4228484-3 (DE-588)4164825-0 |
| title | Computational invariant theory |
| title_auth | Computational invariant theory |
| title_exact_search | Computational invariant theory |
| title_full | Computational invariant theory Harm Derksen ; Gregor Kemper |
| title_fullStr | Computational invariant theory Harm Derksen ; Gregor Kemper |
| title_full_unstemmed | Computational invariant theory Harm Derksen ; Gregor Kemper |
| title_short | Computational invariant theory |
| title_sort | computational invariant theory |
| topic | Kommutativer Ring - Invariantentheorie - Computeralgebra Computeralgebra (DE-588)4010449-7 gnd Invariantentheorie (DE-588)4162209-1 gnd Algebraische Transformationsgruppe (DE-588)4228484-3 gnd Kommutativer Ring (DE-588)4164825-0 gnd |
| topic_facet | Kommutativer Ring - Invariantentheorie - Computeralgebra Computeralgebra Invariantentheorie Algebraische Transformationsgruppe Kommutativer Ring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009800374&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV014336202 (DE-604)BV024126459 |
| work_keys_str_mv | AT derksenharm computationalinvarianttheory AT kempergregor computationalinvarianttheory |