Sphere packings, lattices and groups:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1999
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften
290 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | LXXIV, 703 S. graph. Darst. |
| ISBN: | 0387985859 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804126984017543168 |
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| adam_text | J.H. CONWAY N.J.A. SLOANE SPHERE PACKINGS, LATTICES AND GROUPS THIRD
EDITION WITH ADDITIONAL CONTRIBUTIONS BY E. BANNAI, R.E. BORCHERDS, J.
LEECH, S.P. NORTON, A.M. ODLYZKO, R.A. PARKER, L. QUEEN AND B.B. VENKOV
WITH 112 ILLUSTRATIONS SPRINGER CONTENTS PREFACE TO FIRST EDITION V
PREFACE TO THIRD EDITION XV LIST OF SYMBOLS LXI CHAPTER 1 SPHERE
PACKINGS AND KISSING NUMBERS J.H. CONWAY AND N.J.A. SLOANE 1 THE SPHERE
PACKING PROBLEM I I PACKING BALL BEARINGS 1 .2 LATTICE PACKINGS 3 3
NONLATTICE PACKINGS 7 4 /7-DIMENSIONAL PACKINGS 8 5 SPHERE PACKING
PROBLEM*SUMMARY OF RESULTS 12 2. THE KISSING NUMBER PROBLEM 21 2.1 THE
PROBLEM OF THE THIRTEEN SPHERES 21 2.2 KISSING NUMBERS IN OTHER
DIMENSIONS 21 2.3 SPHERICAL CODES 24 2.4 THE CONSTRUCTION OF SPHERICAL
CODES FROM SPHERE PACKINGS 26 2.5 THE CONSTRUCTION OF SPHERICAL CODES
FROM BINARY CODES ... 26 2.6 BOUNDS ON A(/I,J ) 27 APPENDIX: PLANETARY
PERTURBATIONS 29 CHAPTER 2 COVERINGS, LATTICES AND QUANTIZERS J.H.
CONWAY AND N.J.A. SLOANE 31 1. THE COVERING PROBLEM 31 1.1 COVERING
SPACE WITH OVERLAPPING SPHERES 31 1.2 THE COVERING RADIUS AND THE
VORONOI CELLS 33 1.3 COVERING PROBLEM*SUMMARY OF RESULTS 36 1.4
COMPUTATIONAL DIFFICULTIES IN PACKINGS AND COVERINGS 40 LXV CONTENTS 2.
LATTICES, QUADRATIC FORMS AND NUMBER THEORY 41 2.1 THE NORM OF A VECTOR
41 2.2 QUADRATIC FORMS ASSOCIATED WITH A LATTICE 42 2.3 THETA SERIES AND
CONNECTIONS WITH NUMBER THEORY 44 2.4 INTEGRAL LATTICES AND QUADRATIC
FORMS 47 2.5 MODULAR FORMS 50 2.6 COMPLEX AND QUATERNIONIC LATTICES 52
3. QUANTIZERS 56 3.1 QUANTIZATION, ANALOG-TO-DIGITAL CONVERSION AND DATA
COMPRESSION 56 3.2 THE QUANTIZER PROBLEM 59 3.3 QUANTIZER
PROBLEM*SUMMARY OF RESULTS 59 CHAPTER 3 CODES, DESIGNS AND GROUPS J.H.
CONWAY AND N.J.A. SLOANE 63 1. THE CHANNEL CODING PROBLEM 63 1.1 THE
SAMPLING THEOREM 63 1.2 SHANNON S THEOREM 66 1.3 ERROR PROBABILITY 69
1.4 LATTICE CODES FOR THE GAUSSIAN CHANNEL 71 2. ERROR-CORRECTING CODES
75 2.1 THE ERROR-CORRECTING CODE PROBLEM 75 2.2 FURTHER DEFINITIONS FROM
CODING THEORY 77 2.3 REPETITION, EVEN WEIGHT AND OTHER SIMPLE CODES 79
2.4 CYCLIC CODES 79 2.5 BCH AND REED-SOLOMON CODES 81 2.6 JUSTESEN CODES
82 2.7 REED-MULLER CODES 83 2.8 QUADRATIC RESIDUE CODES 84 2.9 PERFECT
CODES 85 2.10 THE PLESS DOUBLE CIRCULANT CODES 86 2.11 GOPPA CODES AND
CODES FROM ALGEBRAIC CURVES 87 2.12 NONLINEAR CODES 87 2.13 HADAMARD
MATRICES 87 3. R-DESIGNS, STEINER SYSTEMS AND SPHERICAL F-DESIGNS 88 3.1
/-DESIGNS AND STEINER SYSTEMS 88 3.2 SPHERICAL R-DESIGNS 89 4. THE
CONNECTIONS WITH GROUP THEORY 90 4.1 THE AUTOMORPHISM GROUP OF A LATTICE
90 4.2 CONSTRUCTING LATTICES AND CODES FROM GROUPS 92 CHAPTER 4 CERTAIN
IMPORTANT LATTICES AND THEIR PROPERTIES J.H. CONWAY AND N.J.A. SLOANE 94
1. INTRODUCTION 94 2. REFLECTION GROUPS AND ROOT LATTICES 95 3. GLUING
THEORY 99 CONTENTS LXVI 4. NOTATION; THETA FUNCTIONS 101 4.1 JACOBI
THETA FUNCTIONS 102 5. THE ^-DIMENSIONAL CUBIC LATTICE Z 106 6. THE
^-DIMENSIONAL LATTICES A A AND A* 108 6.1 THE LATTICE A N 108 6.2 THE
HEXAGONAL LATTICE 110 6.3 THE FACE-CENTERED CUBIC LATTICE 112 6.4 THE
TETRAHEDRAL OR DIAMOND PACKING 113 6.5 THE HEXAGONAL CLOSE-PACKING 113
6.6 THE. DUAL LATTICE A* 115 6.7 THE BODY-CENTERED CUBIC LATTICE 116 7.
THE H-DIMENSIONAL LATTICES * AND D* 117 7.1 THE LATTICE D N 117 7.2
THE FOUR-DIMENSIONAL LATTICE D 4 118 7.3 THE PACKING D N 119 7.4 THE
DUAL LATTICE D* 120 8. THE LATTICES E B , E 7 AND 8 120 8.1 THE
8-DIMENSIONAL LATTICE * 120 8.2 THE 7-DIMENSIONAL LATTICES 7 AND E?
124 8.3 THE 6-DIMENSIONAL LATTICES 6 AND ET 125 9. THE 12-DIMENSIONAL
COXETER-TODD LATTICE K N 127 10. THE 16-DIMENSIONAL BARNES-WALL LATTICE
A, 6 129 11. THE 24-DIMENSIONAL LEECH LATTICE A 24 131 CHAPTER 5 SPHERE
PACKING AND ERROR-CORRECTING CODES J. LEECH AND N.J.A. SLOANE 136 1.
INTRODUCTION 136 1.1 THE COORDINATE ARRAY OF A POINT 137 2. CONSTRUCTION
A 137 2.1 THE CONSTRUCTION 137 2.2 CENTER DENSITY 137 2.3 KISSING
NUMBERS 138 2.4 DIMENSIONS 3 TO 6 138 2.5 DIMENSIONS 7 AND 8 138 2.6
DIMENSIONS 9 TO 12 139 2.7 COMPARISON OF LATTICE AND NONLATTICE PACKINGS
140 3. CONSTRUCTION B 141 3.1 THE CONSTRUCTION 141 3.2 CENTER DENSITY
AND KISSING NUMBERS 141 3.3 DIMENSIONS 8, 9 AND 12 142 3.4 DIMENSIONS 15
TO 24 142 4. PACKINGS BUILT UP BY LAYERS 142 4.1 PACKING BY LAYERS 142
4.2 DIMENSIONS 4 TO 7 144 4.3 DIMENSIONS 11 AND 13 TO 15 144 4.4 DENSITY
DOUBLING AND THE LEECH LATTICE A 24 145 4.5 CROSS SECTIONS OF A 24 145
5. OTHER CONSTRUCTIONS FROM CODES 146 LXVII CONTENTS 5.1 A CODE OF
LENGTH 40 146 5.2 A LATTICE PACKING IN R 40 147 5.3 CROSS SECTIONS OF A
40 148 5.4 PACKINGS BASED ON TERNARY CODES 148 5.5 PACKINGS OBTAINED
FROM THE PLESS CODES 148 5.6 PACKINGS OBTAINED FROM QUADRATIC RESIDUE
CODES 149 5.7 DENSITY DOUBLING IN R 24 AND R 48 149 6. CONSTRUCTION C
150 6.1 THE CONSTRUCTION 150 6.2 DISTANCE BETWEEN CENTERS 150 6.3 CENTER
DENSITY 150 6.4 KISSING NUMBERS 151 6.5 PACKINGS OBTAINED FROM
REED-MULLER CODES 151 6.6 PACKINGS OBTAINED FROM BCH AND OTHER CODES 152
6.7 DENSITY OF BCH PACKINGS 153 6.8 PACKINGS OBTAINED FROM JUSTESEN
CODES 155 CHAPTER 6 LAMINATED LATTICES J.H. CONWAY AND N.J.A. SLOANE 157
1. INTRODUCTION 157 2. THE MAIN RESULTS 163 3. PROPERTIES OF A O TO A 8
168 4. DIMENSIONS 9 TO 16 170 5. THE DEEP HOLES IN A, 6 174 6.
DIMENSIONS 17 TO 24 176 7. DIMENSIONS 25 TO 48 177 APPENDIX: THE BEST
INTEGRAL LATTICES KNOWN 179 CHAPTER 7 FURTHER CONNECTIONS BETWEEN CODES
AND LATTICES N.J.A. SLOANE 181 1. INTRODUCTION 181 2. CONSTRUCTION A 182
3. SELF-DUAL (OR TYPE I) CODES AND LATTICES .: 185 4. EXTREMAL TYPE I
CODES AND LATTICES 189 5. CONSTRUCTIONB 191 6. TYPE II CODES AND
LATTICES 191 7. EXTREMAL TYPE II CODES AND LATTICES 193 8. CONSTRUCTIONS
A AND B FOR COMPLEX LATTICES 197 9. SELF-DUAL NONBINARY CODES AND
COMPLEX LATTICES 202 10. EXTREMAL NONBINARY CODES AND COMPLEX LATTICES
205 CHAPTER 8 ALGEBRAIC CONSTRUCTIONS FOR LATTICES J.H. CONWAY AND
N.J.A. SLOANE 206 1. INTRODUCTION 206 2. THE ICOSIANS AND THE LEECH
LATTICE 207 CONTENTS LXVIII 2.1 THE ICOSIAN GROUP 207 2.2 THE ICOSIAN
AND TURYN-TYPE CONSTRUCTIONS FOR THE LEECH LATTICE 210 3. A GENERAL
SETTING FOR CONSTRUCTION A, AND QUEBBEMANN S 64-DIMENSIONAL LATTICE 211
4. LATTICES OVER Z[E 4 ], AND QUEBBEMANN S 32-DIMENSIONAL LATTICE 215
5. MCKAY S 40-DIMENSIONAL EXTREMAL LATTICE 221 6. REPEATED DIFFERENCES
AND CRAIG S LATTICES 222 7. LATTICES FROM ALGEBRAIC NUMBER THEORY 224
7.1 INTRODUCTION 224 7.2 LATTICES FROM THE TRACE NORM 224 7.3 EXAMPLES
FROM CYCLOTOMIC FIELDS 227 7.4 LATTICES FROM CLASS FIELD TOWERS 227 7.5
UNIMODULAR LATTICES WITH AN AUTOMORPHISM OF PRIME ORDER 229 8.
CONSTRUCTIONS D AND D 232 8.1 CONSTRUCTION D 232 8.2 EXAMPLES 233 8.3
CONSTRUCTION D 235 9. CONSTRUCTION E 236 10. EXAMPLES OF CONSTRUCTION E
238 CHAPTER 9 BOUNDS FOR CODES AND SPHERE PACKINGS N.J.A. SLOANE 245 1.
INTRODUCTION 245 2. ZONAL SPHERICAL FUNCTIONS 249 2.1 THE
2-POINT-HOMOGENEOUS SPACES 250 2.2 REPRESENTATIONS OF G 252 2.3 ZONAL
SPHERICAL FUNCTIONS 253 2.4 POSITIVE-DEFINITE DEGENERATE KERNELS 256 3.
THE LINEAR PROGRAMMING BOUNDS 257 3.1 CODES AND THEIR DISTANCE
DISTRIBUTIONS 257 3.2 THE LINEAR PROGRAMMING BOUNDS 258 3.3 BOUNDS FOR
ERROR-CORRECTING CODES 260 3.4 BOUNDS FOR CONSTANT-WEIGHT CODES 263 3.5
BOUNDS FOR SPHERICAL CODES AND SPHERE PACKINGS 263 4. OTHER BOUNDS 265
CHAPTER 10 THREE LECTURES ON EXCEPTIONAL GROUPS J.H. CONWAY 267 1. FIRST
LECTURE 267 1.1 SOME EXCEPTIONAL BEHAVIOR OF THE GROUPS L N (Q) 267 1.2
THE CASE P = 3 269 1.3 THE CASE P = 5 269 1.4 THECASEP = 7 269 LXIX
CONTENTS 1.5 THECASE/?=LL 271 1.6 A PRESENTATION FOR M L2 273 1.7
JANKO S GROUP OF ORDER 175560 273 2. SECOND LECTURE 274 2.1 THE MATHIEU
GROUP M 24 274 2.2 THE STABILIZER OF AN OCTAD 276 2.3 THE STRUCTURE OF
THE GOLAY CODE * 24 278 2.4 THE STRUCTURE OF P (D.)K 24 278 2.5 THE
MAXIMAL SUBGROUPS OF M 24 279 2.6 THE STRUCTURE OF P(Q) 283 3. THIRD
LECTURE 286 3.1 THE GROUP CO 0 = 0 AND SOME OF ITS SUBGROUPS 286 3.2 THE
GEOMETRY OF THE LEECH LATTICE 286 3.3 THE GROUP 0 AND ITS SUBGROUP N 287
3.4 SUBGROUPS OF 0 290 3.5 THE HIGMAN-SIMS AND MCLAUGHLIN GROUPS 292 3.6
THE GROUP CO, = -3 293 3.7 INVOLUTIONS IN -0 294 3.8 CONGRUENCES FOR
THETA SERIES 294 3.9 A CONNECTION BETWEEN -0 AND FISCHER S GROUP FI 2I
295 APPENDIX: ON THE EXCEPTIONAL SIMPLE GROUPS 296 CHAPTER 11 THE GOLAY
CODES AND THE MATHIEU GROUPS J.H. CONWAY 299 1. INTRODUCTION 299 2.
DEFINITIONS OF THE HEXACODE 300 3. JUSTIFICATION OF A HEXACODEWORD 302
4. COMPLETING A HEXACODEWORD 302 5. THE GOLAY CODE % LT AND THE MOG 303
6. COMPLETING OCTADS FROM 5 OF THEIR POINTS 305 7. THE MAXIMAL SUBGROUPS
OF M 24 307 8. THE PROJECTIVE SUBGROUP L 2 (23) 308 9. THE SEXTET GROUP
2 6 :3S 6 309 10. THE OCTAD GROUP 2 4 : A 8 311 11. THE TRIAD GROUP AND
THE PROJECTIVE PLANE OF ORDER 4 314 12. THE TRIO GROUP 2 : (S 3 X L 2
(7)) 316 13. THE OCTERN GROUP 318 14. THE MATHIEU GROUP M 2 , 319 15.
THE GROUP M 22 : 2 319 16. THE GROUP M I2 , THE TETRACODE AND THE
MINIMOG 320 17. PLAYING CARDS AND OTHER GAMES 323 18. FURTHER
CONSTRUCTIONS FOR M 12 327 CHAPTER 12 A CHARACTERIZATION OF THE LEECH
LATTICE J.H. CONWAY 331 CONTENTS LXX CHAPTER 13 BOUNDS ON KISSING
NUMBERS A.M. ODLYZKO AND N.J.A. SLOANE 337 1. A GENERAL UPPER BOUND 337
2. NUMERICAL RESULTS 338 CHAPTER 14 UNIQUENESS OF CERTAIN SPHERICAL
CODES E. BANNAL AND N.J.A. SLOANE 340 1. INTRODUCTION 340 2. UNIQUENESS
OF THE CODE OF SIZE 240 IN FL 8 342 3. UNIQUENESS OF THE CODE OF SIZE 56
IN FT 7 344 4. UNIQUENESS OF THE CODE OF SIZE 196560 IN FL 24 345 5.
UNIQUENESS OF THE CODE OF SIZE 4600 IN N 23 349 CHAPTER 15 ON THE
CLASSIFICATION OF INTEGRAL QUADRATIC FORMS J.H. CONWAY AND N.J.A. SLOANE
352 1. INTRODUCTION 352 2. DEFINITIONS 354 2.1 QUADRATIC FORMS 354 2.2
FORMS AND LATTICES; INTEGRAL EQUIVALENCE 355 3. THE CLASSIFICATION OF
BINARY QUADRATIC FORMS 356 3.1 CYCLES OF REDUCED FORMS 356 3.2 DEFINITE
BINARY FORMS 357 3.3 INDEFINITE BINARY FORMS 359 3.4 COMPOSITION OF
BINARY FORMS 364 3.5 GENERA AND SPINOR GENERA FOR BINARY FORMS 366 4.
THE P-ADIC NUMBERS 366 4.1 THE P-ADIC NUMBERS 367 4.2 P-ADIC SQUARE
CLASSES 367 4.3 AN EXTENDED JACOBI-LEGENDRE SYMBOL 368 4.4
DIAGONALIZATION OF QUADRATIC FORMS 369 5. RATIONAL INVARIANTS OF
QUADRATIC FORMS 370 5.1 INVARIANTS AND THE ODDITY FORMULA 370 5.2
EXISTENCE OF RATIONAL FORMS WITH PRESCRIBED INVARIANTS 372 5.3 THE
CONVENTIONAL FORM OF THE HASSE-MINKOWSKI INVARIANT 373 6. THE INVARIANCE
AND COMPLETENESS OF THE RATIONAL INVARIANTS 373 6.1 THE P-ADIC
INVARIANTS FOR BINARY FORMS 373 6.2 THE P-ADIC INVARIANTS FOR -ARY
FORMS 375 6.3 THE PROOF OF THEOREM 7 377 7. THE GENUS AND ITS INVARIANTS
378 7.1 P-ADIC INVARIANTS 378 7.2 THE P-ADIC SYMBOL FOR A FORM 379 LXXI
CONTENTS 7.3 2-ADIC INVARIANTS 380 7.4 THE 2-ADIC SYMBOL 380 7.5
EQUIVALENCES BETWEEN JORDAN DECOMPOSITIONS 381 7.6 A CANONICAL 2-ADIC
SYMBOL 382 7.7 EXISTENCE OF FORMS WITH PRESCRIBED INVARIANTS 382 7.8 A
SYMBOL FOR THE GENUS 384 8. CLASSIFICATION OF FORMS OF SMALL DETERMINANT
AND OF P-ELEMENTARY FORMS 385 8.1 FORMS OF SMALL DETERMINANT 385 8.2
P-ELEMENTARY FORMS 386 9. THE SPINOR GENUS 388 9.1 INTRODUCTION 388 9.2
THE SPINOR GENUS 389 9.3 IDENTIFYING THE SPINOR KERNEL 390 9.4 NAMING
THE SPINOR OPERATORS FOR THE GENUS OF/ 390 9.5 COMPUTING THE SPINOR
KERNEL FROM THE P-AD C SYMBOLS 391 9.6 TRACTABLE AND IRRELEVANT PRIMES
392 9.7 WHEN IS THERE ONLY ONE CLASS IN THE GENUS? 393 10. THE
CLASSIFICATION OF POSITIVE DEFINITE FORMS 396 10.1 MINKOWSKI REDUCTION
396 10.2 THE KNESER GLUING METHOD 399 10.3 POSITIVE DEFINITE FORMS OF
DETERMINANT 2 AND 3 399 11. COMPUTATIONAL COMPLEXITY 402 CHAPTER 16
ENUMERATION OF UNIMODULAR LATTICES J.H. CONWAY AND N.J.A. SLOANE 406 1.
THE NIEMEIER LATTICES AND THE LEECH LATTICE 406 2. THE MASS FORMULAE FOR
LATTICES 408 3. VERIFICATIONS OF NIEMEIER S LIST 410 4. THE ENUMERATION
OF UNIMODULAR LATTICES IN DIMENSIONS N =S 23 413 CHAPTER 17 THE
24-DIMENSIONAL ODD UNIMODULAR LATTICES R.E. BORCHERDS 421 CHAPTER 18
EVEN UNIMODULAR 24-DIMENSIONAL LATTICES B.B. VENKOV 429 1. INTRODUCTION
429 2. POSSIBLE CONFIGURATIONS OF MINIMAL VECTORS 430 3. ON LATTICES
WITH ROOT SYSTEMS OF MAXIMAL RANK 433 4. CONSTRUCTION OF THE NIEMEIER
LATTICES 436 5. A CHARACTERIZATION OF THE LEECH LATTICE 439 CONTENTS
LXXII CHAPTER 19 ENUMERATION OF EXTREMAL SELF-DUAL LATTICES J.H. CONWAY,
A.M. ODLYZKO AND N.J.A. SLOANE 441 1. DIMENSIONS 1-16 441 2. DIMENSIONS
17-47 441 3. DIMENSIONS N S= 48 443 CHAPTER 20 FINDING THE CLOSEST
LATTICE POINT J.H. CONWAY AND N.J.A. SLOANE 445 1. INTRODUCTION 445 2.
THE LATTICES Z , D N AND A 446 3. DECODING UNIONS OF COSETS 448 4. SOFT
DECISION DECODING FOR BINARY CODES 449 5. DECODING LATTICES OBTAINED
FROM CONSTRUCTION A 450 6. DECODING 8 450 CHAPTER 21 VORONOI CELLS OF
LATTICES AND QUANTIZATION ERRORS J.H. CONWAY AND N.J.A. SLOANE 451 1.
INTRODUCTION 451 2. SECOND MOMENTS OF POLYTOPES 453 2.A DIRICHLET S
INTEGRAL 453 2.B GENERALIZED OCTAHEDRON OR CROSSPOLYTOPE 454 2.C THE
N-SPHERE 454 2.D ^-DIMENSIONAL SIMPLICES 454 2.E REGULAR SIMPLEX 455 2.F
VOLUME AND SECOND MOMENT OF A POLYTOPE IN TERMS OF ITS FACES 455 2.G
TRUNCATED OCTAHEDRON 456 2.H SECOND MOMENT OF REGULAR POLYTOPES 456 2.1
REGULAR POLYGONS 457 2.J ICOSAHEDRON AND DODECAHEDRON 457 2.K THE
EXCEPTIONAL 4-DIMENSIONAL POLYTOPES 457 3. VORONOI CELLS AND THE MEAN
SQUARED ERROR OF LATTICE QUANTIZERS 458 3. A THE VORONOI CELL OF A ROOT
LATTICE 458 3.B VORONOI CELL FOR A A 461 3.C VORONOI CELL FOR D N (N S
4) 464 3.D VORONOI CELLS FOR *,** 464 3.E VORONOI CELL FOR D* 465 3.F
VORONOI CELL FOR A* 474 3.G THE WALLS OF THE VORONOI CELL 476 CHAPTER 22
A BOUND FOR THE COVERING RADIUS OF THE LEECH LATTICE S.P. NORTON 478
LXXIII CONTENTS CHAPTER 23 THE COVERING RADIUS OF THE LEECH LATTICE J.H.
CONWAY, R.A. PARKER AND N.J.A. SLOANE 480 1. INTRODUCTION 480 2. THE
COXETER-DYNKIN DIAGRAM OF A HOLE 482 3. HOLES WHOSE DIAGRAM CONTAINS AN
A N SUBGRAPH 486 4. HOLES WHOSE DIAGRAM CONTAINS A D N SUBGRAPH 497 5.
HOLES WHOSE DIAGRAM CONTAINS AN E N SUBGRAPH 504 CHAPTER 24 TWENTY-THREE
CONSTRUCTIONS FOR THE LEECH LATTICE J.H. CONWAY AND N.J.A. SLOANE 508 1.
THE HOLY CONSTRUCTIONS 508 2. THE ENVIRONS OF A DEEP HOLE 512 CHAPTER
25 THE CELLULAR STRUCTURE OF THE LEECH LATTICE R.E. BORCHERDS, J.H.
CONWAY AND L. QUEEN 515 1. INTRODUCTION 515 2. NAMES FOR THE HOLES 515
3. THE VOLUME FORMULA 516 4. THE ENUMERATION OF THE SMALL HOLES 521
CHAPTER 26 LORENTZIAN FORMS FOR THE LEECH LATTICE J.H. CONWAY AND N.J.A.
SLOANE 524 1. THE UNIMODULAR LORENTZIAN LATTICES 524 2. LORENTZIAN
CONSTRUCTIONS FOR THE LEECH LATTICE 525 CHAPTER 27 THE AUTOMORPHISM
GROUP OF THE 26-DIMENSIONAL EVEN UNIMODULAR LORENTZIAN LATTICE J.H.
CONWAY 529 1. INTRODUCTION 529 2. THE MAIN THEOREM 530 CHAPTER 28 LEECH
ROOTS AND VINBERG GROUPS J.H. CONWAY AND N.J.A. SLOANE 534 1. THE LEECH
ROOTS 534 2. ENUMERATION OF THE LEECH ROOTS 543 3. THE LATTICES I NL FOR
S 19 549 4. VINBERG S ALGORITHM AND THE INITIAL BATCHES OF FUNDAMENTAL
ROOTS 549 5. THE LATER BATCHES OF FUNDAMENTAL ROOTS 552 CONTENTS LXXIV
CHAPTER 29 THE MONSTER GROUP AND ITS 196884-DIMENSIONAL SPACE J.H.
CONWAY 556 1. INTRODUCTION 556 2. THE GOLAY CODE * AND THE PARKER LOOP
9 558 3. THE MATHIEU GROUP A/ 24 ; THE STANDARD AUTOMORPHISMS OF 9 558
4. THE GOLAY COCODE %* AND THE DIAGONAL AUTOMORPHISMS ... 558 5. THE
GROUP N OF TRIPLE MAPS 559 6. THE KERNEL K AND THE HOMOMORPHISM G^ G
559 7. THE STRUCTURES OF VARIOUS SUBGROUPS OF N 559 8. THE LEECH LATTICE
A 24 AND THE GROUP Q X 560 9. SHORT ELEMENTS 561 10. THE BASIC
REPRESENTATIONS OF N 561 11. THE DICTIONARY 562 12. THE ALGEBRA ._^ 563
13. THE DEFINITION OF THE MONSTER GROUP G, AND ITS FINITENESS 563 14.
IDENTIFYING THE MONSTER 564 APPENDIX 1. COMPUTING IN 3 565 APPENDIX 2.
A CONSTRUCTION FOR 9 56 5 APPENDIX 3. SOME RELATIONS IN Q, 566 APPENDIX
4. CONSTRUCTING REPRESENTATIONS FOR N, 568 APPENDIX 5. BUILDING THE
GROUP G, 569 CHAPTER 30 A MONSTER LIE ALGEBRA? R.E. BORCHERDS, J.H.
CONWAY, L. QUEEN AND N.J.A. SLOANE 570 BIBLIOGRAPHY 574 SUPPLEMENTARY
BIBLIOGRAPHY 642 INDEX 681
|
| any_adam_object | 1 |
| author_GND | (DE-588)119529289 (DE-588)121291553 |
| building | Verbundindex |
| bvnumber | BV012356666 |
| classification_rvk | SK 170 SK 380 |
| classification_tum | MAT 052f MAT 103f MAT 209f |
| ctrlnum | (OCoLC)264049934 (DE-599)BVBBV012356666 |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV012356666 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:26:08Z |
| institution | BVB |
| isbn | 0387985859 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008378503 |
| oclc_num | 264049934 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-824 DE-703 DE-355 DE-BY-UBR DE-29T DE-706 DE-634 DE-83 DE-11 DE-188 DE-898 DE-BY-UBR |
| owner_facet | DE-91G DE-BY-TUM DE-824 DE-703 DE-355 DE-BY-UBR DE-29T DE-706 DE-634 DE-83 DE-11 DE-188 DE-898 DE-BY-UBR |
| physical | LXXIV, 703 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Sphere packings, lattices and groups J. H. Conway ; N. J. A. Sloane. With additional contrib. by E. Bannai ... 3. ed. New York [u.a.] Springer 1999 LXXIV, 703 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 290 Gittertheorie (DE-588)4157394-8 gnd rswk-swf Kugelpackung (DE-588)4165929-6 gnd rswk-swf Gitter Mathematik (DE-588)4157375-4 gnd rswk-swf Überdeckung Mathematik (DE-588)4186551-0 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Packungsproblem (DE-588)4173057-4 gnd rswk-swf Quadratische Form (DE-588)4128297-8 gnd rswk-swf Klassifikation (DE-588)4030958-7 gnd rswk-swf Gitter Mathematik (DE-588)4157375-4 s Klassifikation (DE-588)4030958-7 s DE-604 Überdeckung Mathematik (DE-588)4186551-0 s Quadratische Form (DE-588)4128297-8 s Kugelpackung (DE-588)4165929-6 s Kombinatorik (DE-588)4031824-2 s Gittertheorie (DE-588)4157394-8 s 1\p DE-604 Packungsproblem (DE-588)4173057-4 s 2\p DE-604 3\p DE-604 Conway, John Horton 1937-2020 Sonstige (DE-588)119529289 oth Sloane, Neil J. A. 1939- Sonstige (DE-588)121291553 oth Grundlehren der mathematischen Wissenschaften 290 (DE-604)BV000000395 290 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008378503&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sphere packings, lattices and groups Grundlehren der mathematischen Wissenschaften Gittertheorie (DE-588)4157394-8 gnd Kugelpackung (DE-588)4165929-6 gnd Gitter Mathematik (DE-588)4157375-4 gnd Überdeckung Mathematik (DE-588)4186551-0 gnd Kombinatorik (DE-588)4031824-2 gnd Packungsproblem (DE-588)4173057-4 gnd Quadratische Form (DE-588)4128297-8 gnd Klassifikation (DE-588)4030958-7 gnd |
| subject_GND | (DE-588)4157394-8 (DE-588)4165929-6 (DE-588)4157375-4 (DE-588)4186551-0 (DE-588)4031824-2 (DE-588)4173057-4 (DE-588)4128297-8 (DE-588)4030958-7 |
| title | Sphere packings, lattices and groups |
| title_auth | Sphere packings, lattices and groups |
| title_exact_search | Sphere packings, lattices and groups |
| title_full | Sphere packings, lattices and groups J. H. Conway ; N. J. A. Sloane. With additional contrib. by E. Bannai ... |
| title_fullStr | Sphere packings, lattices and groups J. H. Conway ; N. J. A. Sloane. With additional contrib. by E. Bannai ... |
| title_full_unstemmed | Sphere packings, lattices and groups J. H. Conway ; N. J. A. Sloane. With additional contrib. by E. Bannai ... |
| title_short | Sphere packings, lattices and groups |
| title_sort | sphere packings lattices and groups |
| topic | Gittertheorie (DE-588)4157394-8 gnd Kugelpackung (DE-588)4165929-6 gnd Gitter Mathematik (DE-588)4157375-4 gnd Überdeckung Mathematik (DE-588)4186551-0 gnd Kombinatorik (DE-588)4031824-2 gnd Packungsproblem (DE-588)4173057-4 gnd Quadratische Form (DE-588)4128297-8 gnd Klassifikation (DE-588)4030958-7 gnd |
| topic_facet | Gittertheorie Kugelpackung Gitter Mathematik Überdeckung Mathematik Kombinatorik Packungsproblem Quadratische Form Klassifikation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008378503&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT conwayjohnhorton spherepackingslatticesandgroups AT sloaneneilja spherepackingslatticesandgroups |