Orthogonal decompositions and integral lattices:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
<<de>> Gruyter
1994
|
| Series: | De Gruyter expositions in mathematics
15 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 511 - 525 |
| Physical Description: | X, 535 S. graph. Darst. |
| ISBN: | 3110137836 |
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MARC
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| 100 | 1 | |a Kostrikin, Aleksej I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Orthogonal decompositions and integral lattices |c by Alexei I. Kostrikin ; Pham Huu Tiep |
| 264 | 1 | |a Berlin [u.a.] |b <<de>> Gruyter |c 1994 | |
| 300 | |a X, 535 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter expositions in mathematics |v 15 | |
| 500 | |a Literaturverz. S. 511 - 525 | ||
| 650 | 7 | |a Lie, algèbres de |2 ram | |
| 650 | 7 | |a Treillis, théorie des |2 ram | |
| 650 | 4 | |a Lattice theory | |
| 650 | 4 | |a Lie algebras | |
| 650 | 4 | |a Orthogonal decompositions | |
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| 650 | 0 | 7 | |a Verband |g Mathematik |0 (DE-588)4062565-5 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text | Table of Contents
Preface v
Introduction 1
Part I: Orthogonal decompositions of complex simple Lie algebras 11
Chapter 1
Type An 13
1.1 Standard construction of ODs for Lie algebras of type Ap,,,_ 13
1.2 Symplectic spreads and / decompositions 17
1.3 Automorphism groups of / decompositions 25
1.4 The uniqueness problem for ODs of Lie algebras of type An, n 4 31
1.5 The uniqueness problem for orthogonal pairs of subalgebras 37
1.6 A connection with Hecke algebras 49
Commentary 51
Chapter 2
The types Bn, Cn and Dn 56
2.1 Type Cn 56
2.2 Partitions of complete graphs and ^ decompositions of Lie algebras of
types Bn and D,, automorphism groups 64
2.3 Partitions of complete graphs and ^ decompositions of Lie algebras of
types Bn and Dn: admissible partitions 68
2.4 Classification of the irreducible £ decompositions of the Lie algebra of
type D,, 76
Commentary 81
Chapter 3
Jordan subgroups and orthogonal decompositions 84
3.1 General construction of TODs 84
3.2 Root orthogonal decompositions (RODs) 88
3.3 Multiplicative orthogonal decompositions (MODs) 93
Commentary 103
Chapter 4
Irreducible orthogonal decompositions of Lie algebras with special
Coxeter number 107
4.1 The irreducibility condition and the finiteness theorem 107
4.2 General outline of the arguments 110
4.3 Regular automorphisms of prime order and Jordan subgroups 113
4.4 h+ =r. the P case 122
4.5 h + 1 = r: classification of IODs 125
4.6 A characterization of the multiplicative orthogonal decompositions of the
Lie algebra of type D4 131
4.7 The non existence of IODs for Lie algebras of types Cp and Dp 136
Commentary 139
Chapter 5
Classification of irreducible orthogonal decompositions of complex simple
Lie algebras of type An 141
5.1 The S case 142
5.2 The P case. I. Generic position 144
5.3 The P case. II. Afflne obstruction 152
5.4 The f case. III. Completion of the proof 158
Commentary 160
Chapter 6
Classification of irreducible orthogonal decompositions of complex simple
Lie algebras of type Bn 162
6.1 The monomiality of G = Aut(D) 163
6.2 Every IOD is an ^ decomposition 168
6.3 Study of Zs decompositions 176
Commentary 186
Chapter 7
Orthogonal decompositions of semisimple associative algebras 187
7.1 Definitions and examples 187
7.2 The divisibility conjecture 190
7.3 A construction of ODs 195
Commentary 198
Part II: Integral lattices and their automorphism groups 199
Chapter 8
Invariant lattices of type G2 and the finite simple Gi(2 ) 203
8.1 Preliminaries 203
8.2 Invariant lattices in £ 208
8.3 Automorphism groups 216
Commentary 229
Chapter 9
Invariant lattices, the Leech lattice and even unimodular analogues of it
in Lie algebras of type Ap^i 231
9.1 Preliminary results 232
9.2 Classification of indivisible invariant lattices 241
9.3 Metric properties of invariant lattices 248
9.4 The duality picture 253
9.5 Study of unimodular invariant lattices 259
9.6 Automorphism groups of projections of invariant lattices 264
9.7 On the automorphism groups of invariant lattices of type Ap 273
Commentary 282
Chapter 10
Invariant lattices of type Apm_i 285
10.1 Preliminaries 285
10.2 Classification of projections of invariant sublattices to a Cartan subalgebra 293
10.3 The structure of the SL2( ?) module TR/prR 301
10.4 The structure of the SL2(q) modu e YR/q2rR 309
10.5 A series of unimodular invariant lattices 320
10.6 Reduction theorem: statement of results 326
10.7 Invariant lattices of type A,,: the imprimitive case 329
10.8 Invariant lattices of type A,,: the primitive case 339
Commentary 353
Chapter 11
The types B2n i and D2«, 355
11.1 Preliminaries 356
11.2 Possible configurations of root systems 361
11.3 Automorphism groups of lattices: the classes 1Z and 1Z2 366
11.4 Lattices of nonroot type: the case Bt, 383
11.5 Lattices of nonroot type: the case D4 391
11.6 Z forms of Lie algebras of types G2, B3 and D4 403
Commentary 408
Chapter 12
Invariant lattices of types F4 and E , and the finite simple groups £4(3),
n?(3), Fi22 409
12.1 On invariant lattices of type F4 410
12.2 Invariant lattices of type E6: the imprimitive case 411
12.3 Character computation 419
12.4 Invariant lattices of type E(,: the primitive case 432
Commentary 439
Chapter 13
Invariant lattices of type Eg and the finite simple groups F3, L4(5) 440
13.1 The Thompson Smith lattice 440
13.2 Statement of results 443
13.3 The imprimitive case 445
13.4 The primitive case 452
13.5 The representations of SU(q) of degree (q 1)( ?3 l)/2 455
Commentary 469
Chapter 14
Other lattice constructions 471
14.1 A Moufang loop, the Dickson form, and a lattice related to Q7(3) 471
14.2 The Steinberg module for SL2(q) and related lattices 479
14.3 The Weil representations of finite symplectic groups and the Gow Gross
lattices 483
14.4 The basic spin representations of the alternating groups, the Barnes Wall
lattices, and the Gow lattices 487
14.5 Globally irreducible representations and some Mordell Weil lattices.... 493
Commentary 504
Appendix 505
Bibliography 511
Notation 526
Author Index 529
Subject Index 531
|
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| id | DE-604.BV009749595 |
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| indexdate | 2024-07-09T17:40:14Z |
| institution | BVB |
| isbn | 3110137836 |
| language | English |
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| physical | X, 535 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
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| publisher | <<de>> Gruyter |
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| series2 | De Gruyter expositions in mathematics |
| spelling | Kostrikin, Aleksej I. Verfasser aut Orthogonal decompositions and integral lattices by Alexei I. Kostrikin ; Pham Huu Tiep Berlin [u.a.] <<de>> Gruyter 1994 X, 535 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 15 Literaturverz. S. 511 - 525 Lie, algèbres de ram Treillis, théorie des ram Lattice theory Lie algebras Orthogonal decompositions Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Verband Mathematik (DE-588)4062565-5 gnd rswk-swf Orthogonale Zerlegung (DE-588)4361361-5 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s Orthogonale Zerlegung (DE-588)4361361-5 s Verband Mathematik (DE-588)4062565-5 s DE-604 Pham, Huu-Tiep 1963- Verfasser (DE-588)113814895 aut De Gruyter expositions in mathematics 15 (DE-604)BV004069300 15 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006449131&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kostrikin, Aleksej I. Pham, Huu-Tiep 1963- Orthogonal decompositions and integral lattices De Gruyter expositions in mathematics Lie, algèbres de ram Treillis, théorie des ram Lattice theory Lie algebras Orthogonal decompositions Lie-Algebra (DE-588)4130355-6 gnd Verband Mathematik (DE-588)4062565-5 gnd Orthogonale Zerlegung (DE-588)4361361-5 gnd |
| subject_GND | (DE-588)4130355-6 (DE-588)4062565-5 (DE-588)4361361-5 |
| title | Orthogonal decompositions and integral lattices |
| title_auth | Orthogonal decompositions and integral lattices |
| title_exact_search | Orthogonal decompositions and integral lattices |
| title_full | Orthogonal decompositions and integral lattices by Alexei I. Kostrikin ; Pham Huu Tiep |
| title_fullStr | Orthogonal decompositions and integral lattices by Alexei I. Kostrikin ; Pham Huu Tiep |
| title_full_unstemmed | Orthogonal decompositions and integral lattices by Alexei I. Kostrikin ; Pham Huu Tiep |
| title_short | Orthogonal decompositions and integral lattices |
| title_sort | orthogonal decompositions and integral lattices |
| topic | Lie, algèbres de ram Treillis, théorie des ram Lattice theory Lie algebras Orthogonal decompositions Lie-Algebra (DE-588)4130355-6 gnd Verband Mathematik (DE-588)4062565-5 gnd Orthogonale Zerlegung (DE-588)4361361-5 gnd |
| topic_facet | Lie, algèbres de Treillis, théorie des Lattice theory Lie algebras Orthogonal decompositions Lie-Algebra Verband Mathematik Orthogonale Zerlegung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006449131&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004069300 |
| work_keys_str_mv | AT kostrikinalekseji orthogonaldecompositionsandintegrallattices AT phamhuutiep orthogonaldecompositionsandintegrallattices |