Opechowski W. — Crystallographic and metacrystallographic groups :: Электронная библиотека попечительского совета мехмата МГУ

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Opechowski W. — Crystallographic and metacrystallographic groups

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Название: Crystallographic and metacrystallographic groups

Автор: Opechowski W.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 628

Добавлена в каталог: 19.06.2005

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Предметный указатель

      92
      98
      see matrix group
$GL(n, \mathbb C)$       see matrix group
$GL(n, \mathbb Q)$       see matrix group
$GL(n, \mathbb R)$       see atrix group
$GL(n, \mathbb Z)$       see matrix group
$ML(n, \mathbb Z)$       see matrix groups
$n\times 1$ matrix = column matrix consisting of n elements      90
$n\times n$ matrix = matrix consisting of n rows and n columns      13
$r\mathbb Z$ -Bravais class of (3+1)-dimensional point lattices      552
$r\mathbb Z$ -class = restricted arithmetic class      552
$r\mathbb Z$ -equivalent point lattices      552
$r\mathbb Z$ -equivalent restricted Bravais groups      552
      see matrix groups
$SL(n, \mathbb Q)$       see matrix groups
$SL(n, \mathbb R)$       see matrix groups
$SL(n, \mathbb Z)$       see matrix groups
$SO(n) = SO(n, \mathbb R)$       see matrix groups
      see matrix groups
      see matrix groups
      95
-symmetry groups      360
symmetry groups      360
$\mathbb C$ = set of all complex numbers      51 Npr
$\mathbb Q$ = set of all rational numbers      Npr
$\mathbb Q$ -equivalence class of matrix groups      81
$\mathbb R$ = set of all real numbers      Npr; 52
$\mathbb Z$ = set of all integers (positive, zero, and negative)      Npr
$\mathbb Z$ -class = arithmetic class      82
$\mathbb Z$ -class of integral matrix groups      81 219
$\mathbb Z$ -equivalent (= arithmetically equivalent) integral matrix groups      82 219
$\mathbf A$ -groups of space-time rotations      168 173 T6.8
$\mathbf B$ -groups of space-time rotations      168 173 T6.8
$\mathbf E$ -groups of space-time rotations      168 173 T6.8
$\mathbf F(3)$ -class of (3+1)-dimensional superspace groups      556
$\mathbf R$ -equivalent matrix groups      78 79
$\mathbf T(n) = {}^{\mathbf{n}\mathbf T(n)$       195 201
$\mathbf V$       88
$\mathbf V-\mathscr T$ isomorphism      115
$\mathrm{Im} \gamma$       23
$\mathrm{Ker}$ \gamma$      23
$\mathscr A(n)$       110
$\mathscr A_+(n)$       121
$\mathscr B$ -equivalent groups of isometries where 3 is a subgroup of an affine group      122 T4.2
$\mathscr D(n)$       121
$\mathscr D^o(n)$       108
$\mathscr D^s(n)$       117
$\mathscr E(n)$       115
$\mathscr E_+(n)$       121
$\mathscr E_1$       165
$\mathscr E_s$       148 165
$\mathscr N = \mathscr E_s\times\mathscr E_t$       165
$\mathscr N_+$       166
$\mathscr R$       148
$\mathscr R_+$       149
$\mathscr R_p(n)\equiv \mathscr E_p(n)$       116 148
$\mathscr R_{\mathrn{st}}$       166
$\mathscr S(n)$       117
$\mathscr S_+(n)$       121
$\mathscr T$       111
$\mathscr T_{\mathrm{st}}$       165
$\mathscr U$ -groups of space-time rotations      168 173 T6.9
$\mathscr U$ -part of an element of the Newton group      168
$\mu$ -group of rotations      156
$\mu$ -subgroup      156 403
$\nu$ -group of rotations      156
$\nu$ -subgroup      60 156
$\tau$ -group of rotations      156
$\tau$ -subgroup      60 156
Abelian group      11
Abstract group      14
Action of a group on a function space      44 351
Action of a group on a set      44
Action of a group — group action: (A1'')      532
Action of a group — group action: (A1')      531
Action of a group — group action: (A1)      350
Action of a group — group action: (A10)      390
Action of a group — group action: (A12E), (A12I), (A12E'), (A12I')      391
Action of a group — group action: (A13E), (A13I), (A13E'), (A13I')      391
Action of a group — group action: (A14E), (A14I), (A14E'), (A14I')      392
Action of a group — group action: (A15E), (A15I), (A15E'), (A15I')      392
Action of a group — group action: (A16)      401
Action of a group — group action: (A16s)      476
Action of a group — group action: (A17)      409
Action of a group — group action: (A1c)      363
Action of a group — group action: (A2)      351
Action of a group — group action: (A3)      353
Action of a group — group action: (A3bc)      385
Action of a group — group action: (A3c)      363
Action of a group — group action: (A4)      354
Action of a group — group action: (A5)      355
Action of a group — group action: (A5c)      383
Action of a group — group action: (A6)      388
Action of a group — group action: (A7s)      388
Action of a group — group action: (A7t)      388
Action of a group — group action: (A8st)      388
Action of a group — group action: (A8t)      388
Action of a group — group action: (A9)      390
Action of a group — group action: (All)      391
Action of the Newton group on a function of space-time      387
Active interpretation of a matrix equation      107
Additive group of complex numbers      51
Additive group of integers      16
Additive group of real numbers      51
Additive notation for products of elements of an Abelian group      15 88
Adjoint matrix group      77
Adjoint of a matrix      76
Admissible site for a subgroup of a group of isometries      294
Admissible spin at a point      478
Affine class (= geometric class) of groups of rotations of a plane      163
Affine class (= geometric class) of groups of rotations of space      154 156 157 T6.1
Affine class (= geometric class) of groups of rotations of space-time      169 173
Affine class of groups of isometries      122 130 T4.2
Affine class of groups of rotations of space      125 157 T6.1
Affine class of infinite axial groups of rotations of space      159 T6.6
Affine class of infinite axial groups of the space-time rotations      159 T6.11
Affine class of magnetic groups      405
Affine group of an affine space      103 110
Affine normalizer of a space group      283
Affine point space      8 92
Affine properties of lattice groups      205
Affine space underlying a Euclidean point space      98
Affine transformation of an affine point space      110 113
Affine vector space      95
Affine vector space underlying a Euclidean vector space      95
Affinely equivalent (= equivalent) groups of isometries      122 T4.2
AL(n+1)      114
Algebraic structure      8 9
Almost-Euclidean-equivalent space groups      283
Alternating group      34
Alternating representation of a group      30
Alternating representation theorem      30 N13.3 N17.2
Angle between two lines      98
Angle between two translations      116
Angle between two vectors      95
Angle, irrational      161
Angle, rational      161
Anti-identification      358
Anti-inversion      358
Anti-rotation      358
Antiferromagnetic helical spin arrangement      489
Antiferromagnetic solid      490
Antiferromagnetic spin arrangement      483
Antiferromagnetic spin lattice      420
Antilinear transformation      523
Antisymmetry      358 N12.5
Antisymmetry group      360
Antiunitary transformations of a vector space      527
Arithmetic approach to the theory of space groups      198 N8.5

Arithmetic class (= $\mathbb Z$ -class) of finite subgroups of $GL(2, \mathbb Z)$       227
Arithmetic class (= $\mathbb Z$ -class) of integral matrix groups      82 219
Arithmetic class (= $\mathbb Z$ -class) of matrix groups      219
Arithmetic class (= $\mathbb Z$ -class) of space groups      263 266 T9.1.3 T9.2.2 T9.2.3
Arithmetically equivalent (= $\mathbb Z$ -equivalent) integral matrix groups      82 219
Associativity of multiplication of elements of a group      10
Asterisk-equivalent (*-equivalent) line groups      331
Asymmorphic space group      N9.3
Atom complex — point complex      291
Atom lattice = point lattice      196 290
Atom lattice with a basis      291
Atom-complex lattice      291
Atom-site array corresponding to the left-coset array for a site group      291 T10.1.1
Augmented matrix      114 132 N4.3
Augmented-matrix representation of a subgroup of an affine group      114
Augmented-matrix representation of an affine group      114
Aut G      45
Automorphism induced by an element of a group      46
Automorphisms of $GL(n, \mathbb C)$       78
Automorphisms of a group      24 44
Automorphisms of a lattice group      204
Automorphisms of a magnetic lattice group      419
Automorphisms of an algebraic structure      103
Automorphisms of cyclic groups      47
Automorphisms of dihedral groups      48 T2.1.1 T2.1.2
Automorphisms of space groups      282
Automorphisms of the field of complex numbers      52
Automorphisms of the field of real numbers      52
Automorphisms of the space-time group induced by the automorphism of the space-time inversion group      170
Average spin of a spin arrangement      483
Axial group of rotations      159
Axial point group of a space group      250
Axial vector      392
Axial vector function      392
Axis of a coordinate system      93
Axis of a group of proper rotations about a line in space      150
Axis of a helical group      333
Axis of a proper rotation of space      149 155
Axis of a rotatory inversion      151
Axis of an axial group of rotations      159
Basic space group of a (3+1)-dimensional superspace group      549
Basis of a Euclidean vector space      96
Basis of a lattice group      203
Basis of a point lattice      203
Basis of a t-dimensional lattice group      195 201
Basis of a vector space      89
Basis vector      89
Bieberbach's Theorems      196 262 N7.9
Bijection      5
Black-and-white group = two-colour group      62 313 354 374
Bracket symbol of a permutation      31
Bravais class of antiferromagnetic spin lattices      426
Bravais class of d-colour lattice groups      373
Bravais class of d-coloured point lattices      373
Bravais class of ferromagnetic spin lattices      426
Bravais class of lattice groups      214
Bravais class of magnetic lattice groups      402 423 T16.3 T16.4 N16.5
Bravais class of magnetic point lattices      423 T16.3 T16.4
Bravais class of point lattices      214 229 T8.2 T8.3
Bravais class of space groups      263 269
Bravais class of spin lattice groups      517
Bravais classification (= classification into Bravais classes) of lattice groups      205 215
Bravais classification (= classification into Bravais classes) of point lattices      205 214 215
Bravais classification (= classification into Bravais classes) of space groups      269
Bravais flock of affine classes of space groups      269
Bravais flock of arithmetic classes of finite integral matrix groups      227
Bravais flock of arithmetic classes of space groups      268
Bravais flock of proper arithmetic classes of finite integral matrix groups      227
Bravais flock of space groups      263
Bravais group      218
Bravais group of a magnetic point lattice for a magnetic basis      422
Bravais group of a point lattice      220
Bravais group of a point lattice for its basis      217
Bravais lattice = point lattice      197
Bravais space group      218 219 269 T9.2.1
Bravais subclass of a proper affine class of space groups      263 269
Bravais superspace group ((3 + l)-dimensional)      552 T22.1
Bravais system of lattice groups      239
Bravais system of magnetic lattice groups      429
Bravais system of magnetic lattices      429
Bravais system of point lattices      239 240 T8.2 T8.3
Bravais system of space groups      = Bravais-fiock system of space groups 277
Bravais type (= Bravais class) of lattice groups      215
Bravais type (= Bravais class) of point lattices      215
Bravais unit cell      N8.5
Bravais' definition of Bravais classes of point lattices      Npr
Bravais-flock system      240 277
Bravais-flock system (= Bravais system) of affine classes of space groups      269 277 T9.1.3
Bravais-flock system (= Bravais system) of arithmetic classes of space groups      268 277
Bravais-flock system (= Bravais system) of space groups      277
Brillouin zone (first)      N8.8
Cambiant symmetry      360
Carrier space invariant under a group      138
Carrier space of a corepresentation      525
Carrier space of a matrix representation of a group      131 139
Carrier space of a representation      131
Carrier space splitting into a direct sum of invariant subspaces      138
Carrier space, irreducible      138
Cartesian coordinate system      98
Cartesian coordinates of a point      98
Cartesian product of two sets      4
Cayley's theorem      49
Centralizer of a subgroup      25
Centre of a group      20
Centre of inversion      150 152
Centred point lattices      N8.2
Centring a point lattice      234
Chain macromolecule      196
Change-of-basis formulae      91
Change-of-coordinate system formulae      94 99
Character of a matrix representation      136
Character of an element of a group in its matrix representation      136
Characteristic crystallographic orbit for a space group      N10.4
Characteristic equation of a matrix      76
Characteristic subgroup      47
Characteristic subgroup of a lattice group      419
Characteristic values (= eigenvalues) of a matrix      76
Cheshire group = Euclidean nonnalizer of a space group      N9.9
Class (= equivalence class) of conjugate elements of a group      26
Class (= equivalence class) of conjugate permutations      34
Class (= equivalence class) of conjugate subgroups      26
Class (= equivalence class) of magnetic space groups = proper affine class of magnetic space groups      452
Class (= equivalence class) of parallel point sets      190
Class (= equivalence class) of positive definite symmetric matrices determined by a point lattice      208
Class (= equivalence class) of positive definite symmetric quadratic forms determined by a point lattice      207
Class (= equivalence class) of rotation groups associated with a space group      250
Class (= equivalence class) of simple point sets for a group of isometries      293 294
Class = equivalence class      8
Class-equivalent subgroup (= R-subgroup) of a space group      261
Classification label of a geometrical crystal (CLG)      292
Classification label of a physical crystal (CLP)      351 382 490
Classification labels of a NaCl crystal      382
Classification labels of spin arrangements      481 487 510
Classification labels of the spin arrangements in $\mathrm{DyCrO}_3$       492
Classification of coloured polyhedra      N13.7
Classification of the elements of a set      8
Classification of the non-isomorphic non-symmorphic space groups      456 T17.2
Classifications of space groups      262 263 264 276 277
Coholohedral lattice of an R-subgroup of a space group      444
Coholohedral subgroup of a lattice group      422 444
Coholohedral subgroup of a space group      444
Coholohedral sublattice of a lattice      422
Collinear antiferromagnetic spin arrangement      483
Colour function = coloured point set      353 363 375
Colour group      73 353 360 364 N12.9
Colour group of rotations      364 370
Colour groups compared to non-trivial spin groups      515 517
Colour lattice group      364 373
Colour of a point      363
Colour set      363

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