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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Proper affine class of one-dimensional magnetic space groups      T11.1.1
Proper arithmetic class of integral matrix groups      82
Proper congruence class of groups of isometries      T4.2
Proper congruence class of point sets      190 N7.2
Proper holohedral class of groups of rotations      216
Proper holohedral class of matrix groups      239 241
Proper motion = direct isometry      121
Proper O-equivalence class of matrix groups      81
Proper rotation      116 121 148 162
Proper similarity class of groups of isometries      T4.2
Proper similarity class of point sets      190 N7.2
Proper space-group type = proper affine class of space groups      264
Proper subarithmetic class of Bravais groups of magnetic point lattices      424
Proper subgroup      15
Proper subset      3
Proximity cell      N8.8
Q-symmetry groups      360
Quadratic form      96
Quasi-crystal      Npr
Quasi-H-M symbol of a spin point group      510 T20.1
Quasisymmetry groups      360
Quotient group = factor group      19 21
Quotient set      7
r-equivalence class of (3+1)-dimensional Bravais superspace groups      553
r-equivalence class of (3+1)-dimensional superspace groups = superspace-group types      557
R-equivalent elements of a set      7 8
R-subgroup of a space group      260 436 437 449 453
R-supergroup of a space group      260
Rational angle      161
Rational discrete helix      336
Rational helical spin arrangement      489
Ray      521
Real crystal      293
Real linear group      103
Real orthogonal matrix group      79 109
Real vector space      88
Realization of an abstract group      14
Reciprocal bases      211
Reciprocal point lattice associated with a point lattice      211 N8.3
Rectangular Bravais system of point lattices      T8.2
Rectangular Bravais system of space groups      T9.1.3
Rectangular geometric-class system of groups of rotations      T6.7
Rectangular groups of rotations      T6.7
Rectangular ITC-system of space groups      T9.1.3
Rectangular point lattice, centred      224 234
Rectangular point lattice, primitive      224 234
Reduced basis of a point lattice in the sense of Dirichlet      207 212 N8.5
Reduced basis of a point lattice in the sense of Minkowski      N8.5
Reduced colour-group family of a group of isometries      370 T13.1
Reduced family of a group of proper rotations      157 T6.4
Reduced magnetic families of crystallographic magnetic groups of rotations      T15.3 T15.4
Reduced magnetic family of a group of isometries      405
Reduced magnetic family of a lattice group      429
Reduced magnetic superfamily of a group of isometries      405
Reduced matrices of the same form      132
Reduced matrix      132
Reduced metric form of a point lattice in the sense of Dirichlet      212 N8.5
Reduced metric form of a point lattice in the sense of Minkowski      N8.5
Reduced net-group family of a two-dimensional space group      310
Reduced net-group superfamily of a two-dimensional space group      310
Reduced spin-group family of a group of isometries      515
Reduced spin-group family of a group of isometries and of a group of orthogonal transformations      515
Reduced spin-group family of the group      422 T20.1
Reduced superfamily of a group of proper rotations      157
Reduced unit cell of a point lattice      212 213
Reducible group of rotations      159 160
Reducible matrix group      132 135
Reducible representation of a group      135
Reference plane      330
Referring a group of affine transformations to a coordinate system      122
Referring a group of linear transformations to a basis      106 107
Reflection group in space      151
Reflection group of a plane      163
Reflection in a line      163
Reflection in a plane      150
Reflexive relation      6
Regular matrix representation of a group      49
Regular permutation representation of a group      49 70
Relabelling of a bracket symbol of a permutation      35
Relabelling Theorem for Permutations      35
Relation on a set      6 8
Relation on a set, equivalence      6
Relation on a set, reflexive      6
Relation on a set, symmetric      6
Relation on a set, transitive      6
Relativistic crystallographic groups      N7.12
Representation of a group by a group of linear transformations      131 N5.1
Representation of a group by a group of matrices = matrix representation of a group      24 131
Representation of a group by a group of permutations = permutation representation of a group      24
Representation of a matrix group by itself      131
Representation of an affine group by an inhomogeneous linear group      113
Representation space = carrier space of a representation      131
Representations (one-dimensional) of the space-time inversion group      T14.1
Representative of a left coset      19
Representative of a right coset      19
Restricted arithmetic class = rZ-class of restricted Bravais groups      552
Restricted Bravais group of a (3+1)-dimensional point lattice associated with a Bravais group of a three-dimensional point lattice      550
Restriction of a homomorphism of a group to its subgroup      24
Reversal space groups in two dimensions      N12.4
Rhombohedral Bravais system      = trigonal Bravais system
Rhombohedral ITC-system      = trigonal fTC-system
Rhombohedral point lattice      = trigonal point lattice
Right cosets of a subgroup      8 19
Right-handed coordinate systems      120
Rigid motion = isometry      115 N4.4
Rotation = proper or improper rotation      148 149
Rotation at a point of a Euclidean point space      116
Rotation group associated with a space group      250
Rotation matrix      109
Rotation-matrix group associated with a basis      109
Rotational part of an isometry      117 N4.4
Rotatory inversion = rotatory reflection      151
Rotatory reflection      151
Rule for constructing the h-subgroups      64 515
Rule for finding all representations by transitive groups of permutations      74
scalar      88
scalar functions      387 389
Scalar product (= inner product) of two vectors      95
Schoenflies symbols for the groups of rotations      158
Schoenflies symbols for the space groups      279
Schroedinger equation      522
Schur's lemma      141 N5.3
Schwarz's inequality      95
Screw axis      152
Screw displacement      152 259
Self-conjugate subgroup = normal subgroup      26
Semidirect product group      27 52
Semidirect product of $GL(n, \mathbb C)$ and a group of its automorphisms      78 524
Semidirect product of two groups      52 53
Semidirect product of two groups, external      52 56
Semidirect product of two groups, internal      56
Semilinear group of a complex vector space      523
Semilinear transformation      519 523
Senior group of symmetry and antisymmetry      361
Sesquilinear transformation of a complex vector space      523
Set      3
Set associated with a partition of a set      6
Set generated by a group of permutations of a set      38
Set of generating elements (= generators) of a subgroup      17
Set of point lattices associated with a class of positive definite symmetric matrices      209
Set of positive definite symmetric matrices associated with an integral-matrix group      225
Setting of a space group      279
Shifting the origin of a coordinate system      94
Shortest lattice vectors of an n-dimensional point lattice      213
Shubnikov group      358 406
Similar groups of isometries      T4.2
Similar point sets      190 N7.2
Similarity class of groups of isometries      T4.2
Similarity class of point sets      190 N7.2
Similarity group of a Euclidean point space      117

Similarity group of a Euclidean vector space      117
Similarity transformation of a Euclidean point space      117
Simple crystal      196 290 T10.2
Simple group      21 24 Npr
Simple point set      189
Simple point set having some symmetry      192
Simple set      39
Simple spin arrangement      478 482 486
Singleton      3
Site group for a group of isometries      194
Site group of a point      194
Site group of a point (= of an atom site) of a simple crystal      290
Site point group of a point (= of an atom site) of a simple crystal      290
Site space group of a point (= of an atom site) of a simple crystal      291 292
Site symmetry group of a point      194
Space = ordinary space = three-dimensional Euclidean point space      87 101 148
Space group      17 46 187 195 218 219 250
Space group as an extension of a lattice group      256 N9.4
Space groups of a plane      T9.1.3
Space inversion      = inversion
Space of functions      = function space
Space-and-time inversion      166
Space-group type = affine class of space groups      264
Space-only spin group      506
Space-time      8 87 99 101 N3.1
Space-time inversion group      13 166
Space-time orientation preserving group      166
Space-time rotation group      166
Space-time translation group      166
Special element of a set      39
Special inhomogeneous linear group SIL(n)      119
Special inhomogeneous rotation-matrix group associated with a basis      116
Special integral matrix group SL(n, Z)      79
Special linear real matrix group SL(n, R)      79
Special orthogonal-matrix group SO(n)      79 110
Special position of a point      194 304
Special rational matrix group SL(n, Q)      79
Special rotation-matrix group associated with a basis      110
Special unitary matrix group SU(n)      77
Spin = magnetic dipole moment      400
Spin arrangement = magnetic dipole arrangement      356 419 420
Spin arrangement generated by a magnetic lattice group      420
Spin arrangement generated by a magnetic space group      479
Spin group = vector group      354 359 505 N12.6
Spin group of rotations = spin point group      508 515
Spin lattice      420
Spin lattice generated by a lattice group      420
Spin lattice group = spin translation group      508 517
Spin point group = spin group of rotations      508
Spin space      400 509 510
Spin space group      508 510 517 N12.6
Spin translation group = spin lattice group      508
Spin-group classification label of a spin arrangement      510
Spin-group family of a group of isometries      508
Spin-group family of a group of isometries and of a group of orthogonal transformations      508
Spin-only spin group      506
Split extension of a group      52
Square Bravais system of point lattices      T8.2
Square Bravais system of space groups      T9.1.3
Square geometric-class system of groups of rotations      T6.7
Square groups of rotations      T6.7
Square ITC-system of space groups      T9.1.3
Square matrix = $n\times n$ matrix      13
Square point lattice      234
Stabilizer of a point of a Euclidean point space      116
Stabilizer of a point of an affine point space      111
Stabilizer of an element of a set      38
Standard basis of a (1+1)-dimensional point lattice      543
Standard basis of a (3+1)-dimensional point lattice      547 T22.1
Standard basis of a coordinate space      90
Standard basis of a point lattice      235 T8.2 T8.3
Standard basis of, irrational, a (3+1)-dimensional point lattice      550
Standard representation of a discrete group of isometries      476
Standard representation of a magnetic group      476
Standard representation of a magnetic space group      476
Standard representation of the point group of a magnetic space group      477
Standard representation of the point group of a space group      477
Standard rule for constructing $\mu$ -subgroups      61
Standard rule for constructing a colour function      367 376
Standard rule for constructing net groups      309
Standard rule for constructing spin arrangements      479
Standard rule for constructing the magnetic family of a group of isometries      404
Standard set of coset representatives for a space group      281
State vector      522
Stationary state belonging to the energy eigenvalue      522
Stratum of orbits for a group of isometries      295
Stretching factor      117
Strictly $\mathbb Q$ -equivalent matrix groups      81
Strictly $\mathbb R$ -equivalent matrix groups      78
Strictly $\mathbb Z$ -equivalent matrix groups      81
Strictly congruent bases of a Euclidean vector space      110 120
Strictly congruent coordinate systems in a Euclidean point space      120
Strictly congruent groups of isometries      T4.2
Strictly congruent point sets      190
Strictly equivalent groups of isometries      122 T4.2
Strictly equivalent magnetic groups      405
Strictly equivalent net groups      310
Strictly O-equivalent matrix groups      81
Strictly similar groups of isometries      T4.2
Strictly similar point sets      190
Structure of a group      14
Subarithmetic class of Bravais groups of magnetic point lattices      424
Subdirect product associated with two quotient groups      67 320
Subdirect product group associated with a group of proper rotations      174
Subdirect product of two groups      59
Subduced matrix representation of a subgroup = restriction to a subgroup of a group of the latter's homomorphism onto a matrix group      24
Subducing a group of permutations of a subset by a group of permutations of a set      38 191
Subfield      52
Subgroup criterion      16
Subgroup of a group      15
Subgroup of a group generated by a set of elements of the group      17
Subgroup of a group generated by a set of subgroups of a group      18
Subgroup of index 2      29
Subgroup of the space-time rotation group = group of rotations of space-time      169
Subgroups of the direct product of two groups      59
Sublattice coholohedral with a magnetic point lattice      422
Sublattice coholohedral with a point lattice      422
Sublattice of a point lattice      204
Subperiodic group of isometries      196
Subset      3
Subset of a group      16
Subspace (of a vector space) spanned by a set of linearly independent vectors      89
Sum of two vectors      88
Superconducting medium      397
Supercrystal ((3+1)-dimensional)      548
Superfamily of a group      61
Superfamily of a group of proper rotations      157
Supergroup of a group      16
Superspace ((1+1)-dimensional)      544
Superspace ((3+1)-dimensional)      545
Superspace ((3+d)-dimensional)      538
Superspace group      197 199 537
Superspace group ((1+1)-dimensional)      544
Superspace group ((3+1)-dimensional)      547 556 557 T22.2
Superspace group ((3+d)-dimensional)      537
Superspace-group type      557
Surjection      5
Symmetric group of degree n      33
Symmetric group on a set      12 30 32 45
Symmetric matrix      76
Symmetric quadratic form      96
Symmetric relation      6
Symmetry class of point sets      193
Symmetry colour group of a colour function      364
Symmetry elements      37
Symmetry elements of a point set      191. N7.3
Symmetry group and symmetry elements of a subset      37
Symmetry group of a composite crystal      300
Symmetry group of a function in the sense of an action of a group      44
Symmetry group of a line      161

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