Computational methods for representations of groups and algebras: Euroconference in Essen (Germany), April 1 - 5, 1997
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
1999
|
| Series: | Progress in mathematics
173 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 357 S. |
| ISBN: | 3764360631 0817660631 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
I Introductory Articles
1 Classification Problems in the Representation Theory
of Finite-Dimensional Algebras
1.1 Introduction 3
1.2 Algebras, Aggregates and Modules 5
1.3 Quivers and Posets 9
1.4 The Auslander-Reiten Quiver 11
1.5 Representation Types 14
1.6 Strongly simply connected Spectroids of Finite and Tame Repre¬
sentation Type 17
1.7 Thin Modules over completely separating Spectroids 21
2 Noncommutative Grobner Bases, and Projective Resolutions
2.1 Overview 29
2.2 Grobner Bases 29
2.3 Algorithms 36
2.4 Computational Aspects 44
2.5 Modules, Presentations and Resolutions 48
2.6 Applications of Grobner Bases 53
3 Construction of Finite Matrix Groups
3.1 Introduction 61
3.2 A Small Example 62
3.3 Some Variants 64
3.4 Towards a General Method 66
3.5 A Generalization 69
3.6 Thompson s Theorem 71
3.7 The Meataxe 73
3.8 Some more Applications 74
3.9 The Baby Monster 76
3.10 An Analogue for Permutation Groups 76
3.11 Some Applications of the Permutation Group Construction ... 79
3.12 The Monster 80
3.13 A World-Wide-Web Atlas of Group Representations 81
xi
xii Contents
II Keynote Articles
4 Derived Tubularity: a Computational Approach
4.1 Derived Equivalence for Algebras 88
4.2 Reduction of Integral Quadratic Forms 92
4.3 Derived Tubularity: an Algorithm 98
4.4 Examples 101
5 Problems in the Calculation of Group Cohomology
5.1 Introduction 107
5.2 Questions and Conjectures 109
5.3 Some Problems in the Computations 113
5.4 Two Exceptional Cases 116
6 On a Tensor Category for the Exceptional Lie Groups
6.1 Introduction 121
6.2 Tensor Categories 122
6.3 A Representation Category for the General Linear Groups .... 123
6.4 The Exceptional Series 128
6.5 The Category £ 129
6.6 The Exceptional Categories 132
7 Non-Commutative Grobner Bases and Anick s Resolution
7.1 Main Examples 140
7.2 Hilbert Series and global Dimension 140
7.3 Normal Words and Grobner Basis 142
7.4 Graphs, Languages and Monomial Algebras 144
7.5 n—Chains and Poincare series 145
7.6 Anick s Resolution 147
7.7 Finite State Automata and Lie Algebras 148
7.8 Bergman Package under MS-DOS 148
7.9 ANICK - Program for calculating Betti Numbers and Grobner
Bases 149
8 A new Existence Proof of Janko s Simple Group J4
8.1 Introduction 161
8.2 Lempken s Subgroup G= (x, y) of GLi333(ll) 162
8.3 Transformation of G into a Permutation Group 166
8.4 Group Structure of the approximate Centralizer H 167
8.5 The Order of CG(ux) 171
8.6 The Main Result 172
9 The Normalization: a new Algorithm, Implementation and Comparisons
9.1 Introduction 177
9.2 Criterion for Normality 178
9.3 The Normalization Algorithm 179
Contents xiii
9.4 Implementation and Comparisons 181
9.5 Examples 183
10 A Computer Algebra Approach to sheaves over
Weighted Projective Lines
10.1 Introduction 187
10.2 Telescoping Functors 190
10.3 Computation of Telescoping Functors in Ko X 195
11 Open Problems in the Theory of Kazhdan-Lusztig polynomials
11.1 Introduction 201
11.2 The Basic Definitions 201
11.3 Hecke algebras and Kazhdan-Lusztig polynomials 203
11.4 Kazhdan-Lusztig polynomials and Bruhat intervals 204
11.5 Some Problems in Type A 207
12 Relative Trace Ideals and Cohen Macaulay Quotients
12.1 Introduction 211
12.2 Basic Definitions 213
12.3 The Trace Map 215
12.4 Invariant Rings of Permutation Modules 218
12.5 The Regular Representation of Zp 220
12.6 A canonical Trace Ideal and Cohen-Macaulay Quotients 222
13 On Sims Presentation for Lyons Simple Group
13.1 Introduction 235
13.2 The Permutation Group of Degree 8835 156 236
13.3 The Permutation Group of Degree 9606 125 237
13.4 The final Verification 238
14 A Presentation for the Lyons Simple Group
14.1 Introduction 241
14.2 A Presentation for the Lyons Group 242
14.3 A computational Proof 245
14.4 The Large Coset Enumeration 246
15 Reduction of Weakly Definite Unit Forms
15.1 Introduction 251
15.2 Proper Reductions 251
15.3 Restricted Reductions 253
15.4 Critical Vectors 253
15.5 Algorithm for Weak Definiteness 253
xiv Contents
16 Decision Problems in Finitely Presented Groups
16.1 Introduction 259
16.2 The Word Problem 259
16.3 The Conjugacy Problem 262
16.4 The Generalized Word Problem 263
17 Some Algorithms in Invariant Theory of Finite Groups
17.1 Introduction 267
17.2 Calculating Homogeneous Invariants 268
17.3 Constructing Primary Invariants 271
17.4 Calculating Secondary Invariants 274
17.5 Properties of the Invariant Ring 278
18 Coxeter Transformations associated with Finite Dimensional Algebras
18.1 Introduction 287
18.2 Bilinear Lattices 290
18.3 Coxeter Polynomials and Growth 291
18.4 The K-Theory of Canonical Algebras 294
18.5 The K-Theory of Hereditary Algebras 300
18.6 Examples, Problems and Questions 303
19 The 2-Modular Decomposition Numbers of Co-i
19.1 Introduction 309
19.2 Condensation 310
19.3 Condensation of Induced Modules, theoretically 312
19.4 ... and practically 313
19.5 An Application: The 2-Modular Character Table of Co2 315
20 Bimodule and Matrix Problems
20.1 Introduction 323
20.2 The first Example - Bimodule Problems 326
20.3 Differential (Z-) graded Category (D(Z)GC) and Boxes 329
20.4 Reductions 343
20.5 Quadratic Forms 351
|
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| discipline | Mathematik |
| format | Book |
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| genre_facet | Konferenzschrift 1997 Essen |
| id | DE-604.BV012555921 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:29:36Z |
| institution | BVB |
| isbn | 3764360631 0817660631 |
| language | English |
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| physical | XIV, 357 S. |
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| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Computational methods for representations of groups and algebras Euroconference in Essen (Germany), April 1 - 5, 1997 P. Dräxler ... eds. Boston [u.a.] Birkhäuser 1999 XIV, 357 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 173 Algebra (DE-588)4001156-2 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1997 Essen gnd-content Gruppentheorie (DE-588)4072157-7 s Darstellungstheorie (DE-588)4148816-7 s DE-604 Algebra (DE-588)4001156-2 s Dräxler, Peter Sonstige oth Progress in mathematics 173 (DE-604)BV000004120 173 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008525587&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Computational methods for representations of groups and algebras Euroconference in Essen (Germany), April 1 - 5, 1997 Progress in mathematics Algebra (DE-588)4001156-2 gnd Gruppentheorie (DE-588)4072157-7 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4072157-7 (DE-588)4148816-7 (DE-588)1071861417 |
| title | Computational methods for representations of groups and algebras Euroconference in Essen (Germany), April 1 - 5, 1997 |
| title_auth | Computational methods for representations of groups and algebras Euroconference in Essen (Germany), April 1 - 5, 1997 |
| title_exact_search | Computational methods for representations of groups and algebras Euroconference in Essen (Germany), April 1 - 5, 1997 |
| title_full | Computational methods for representations of groups and algebras Euroconference in Essen (Germany), April 1 - 5, 1997 P. Dräxler ... eds. |
| title_fullStr | Computational methods for representations of groups and algebras Euroconference in Essen (Germany), April 1 - 5, 1997 P. Dräxler ... eds. |
| title_full_unstemmed | Computational methods for representations of groups and algebras Euroconference in Essen (Germany), April 1 - 5, 1997 P. Dräxler ... eds. |
| title_short | Computational methods for representations of groups and algebras |
| title_sort | computational methods for representations of groups and algebras euroconference in essen germany april 1 5 1997 |
| title_sub | Euroconference in Essen (Germany), April 1 - 5, 1997 |
| topic | Algebra (DE-588)4001156-2 gnd Gruppentheorie (DE-588)4072157-7 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | Algebra Gruppentheorie Darstellungstheorie Konferenzschrift 1997 Essen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008525587&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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