Conway J.H., Smith D.A. — On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry :: Электронная библиотека попечительского совета мехмата МГУ

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Conway J.H., Smith D.A. — On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry

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Название: On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry

Авторы: Conway J.H., Smith D.A.

Аннотация:

Video game programmers and spacecraft controllers use quaternions to calculate rotation, but Conway and Smith (Lafayette College) stick to the theoretical aspects of these algebras connected with special features of the geometry of complex numbers, and the symmetry of lesser-known octonian algebra

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 159

Добавлена в каталог: 18.11.2009

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

Предметный указатель

Lipschitzian      55
Loop, inverse      83
Loop, Moufang      72 83 87
Magic Square, Freudenthal's      143
Mahler, K.      110
Maximal subgroups of $G_{2}(2)$       134
Metacommutation      61
Metacommutation problem      116
Metacommutation problem, Lipschitzian      117
Metamigration      114 115
Metamigration problem      116
Metamigration problem, Gravesian      117
Metassociation problem      116
Model, factorization on a      57 114
MODULO      2 5
Monotopy      86 87 90
Monotopy, every $SO_{8}$ element is a      90
Monotopy, transitivity and Moup law      87
Moufang loop      83
Moufang, R.      72 88
Moup      see Moufang loop
Multiplication map, bi-, $B_{x}$       73 87 90
Multiplication map, companions for      97
Multiplication map, left, $L_{x}$       73 86
Multiplication map, right, $R_{x}$       73 86
Names for groups, algebraic      36
Names for groups, geometric      36
Neub $\ddot{u}$ ser, J.      48
Non-associative      72 89
Norm, Euclidean      11 100
Notations for groups, algebraic      35 36
Notations for groups, orbifold      14 20 28 36
Number, Catalan      116
Number, Cayley      9
Number, complex      11
Number, of prime factorizations      115
Number, real      3
octahedron      106
Octaves      8 99
Octaves, Gravesian      100
Octaves, Kleinian      103
Octavian (integer)      99 105
Octavian (integer), unit      119
Octavian (integer), unit ring      125
Octonions      5 99
Octonions, and eight - Dimensional geometry      89
Orbifold      20
Order      100 103
Order, containing Gravesians      101
Order, maximal      100 102 103
Orthogonality, even and odd      120
Orthoplex lattice, $D_{n}$       106
P $\acute{o}$ lya, G.      19
Pascal's triangle      60
Pascal, B.      60
Peirce, B.      7
Pfister, A.      78
Polyhedra      36
Polyhedra, regular      30
Polytope, regular      45
Porteous, I.      145
Prime, Eisenstein      16
Prime, factorization      56
Prime, Gaussian      15
Prime, Hurwitzian      56
Prime, octavian      115
Primitive octavian, factorizations of      115
Problem, meta      116
Problem, metacommutation      61
Problem, metamigration      116
Problem, metassociation      116
Projective plane      88
Projective plane, octonion      5 143 144
Projective plane, order 2      137
Quad, and co-quad      119
Quadratic form, multiplicative      79

Quadratic form, non-degenerate      76
Quadratic non-residue      58
Quadratic residue      58
Quasiconjugation      80
Quaternion      5 23
Quaternion, finite groups of      33
Quaternion, subalgebra, what fixes      80
Rankin, R. A.      10 111 116
Rational numbers      3
Real numbers      3
Recombination      61
Reflection      3 11 90
Reflection, in       41
Regular orthoplex      106
Regular polyhedron      26
Regular polytope      43
Regular simplex      106
Rehm's algorithm      111
Rehm, H. P.      99 111
Ring      15
Ring, Kleinian      18
Rodrigues, O.      9 105
Rotation      11
Rotation, simple      6 23 40
Rotation, simple, product of      26
Schafer, R. D.      73
Schl $\ddot{a}$ fli, L.      45
Seifert, H.      48
Similarity      11 23 113
Simplex lattice, $A_{n}$       106
Smith, H. J. S.      105
Smith, W. D.      73
Spherical geometry      26
Spin ${}_{3}$       24
Spin ${}_{4}$       42
Spin ${}_{7}$       95
Spin ${}_{8}$       91 95
Springer, T.      110
Stark, H. M.      18
Stufe of field      79
Subgroups, left and right      44
Symmetry, central      34 36
Symmetry, of algebra      see automorphism
Tait, P.      7
Theorem, 5-multiplication      95
Theorem, Euler's on rotations      24 26
Theorem, Hurwitz classification      67 72 78
Theorem, orbifold Magic      20
Theorem, seven-multiplication      5 93
Theorem, spherical excess      28 (see also Unique factorization)
Threlfall, W.      48
Tits, J.      144
Trace      100
Transformation by , $T_{a}$       98
Translation      3
Triality      5 6 91
Triality, of Spin ${}_{8}$ and $PS O_{8}$       92
Triplet, even and odd      121
Triplet, of octavians      119
Triplet, quaternion      75
Triplex form of hexad      84
Triplex form of isotopy      84 91
Triplex form of relation      84
Unique factorization      3 15 16 61 110
UNIT      11
Unit, Hurwitz      56
Unit, Lipschitz      56
Unit, octavian      119
Unit,Gaussian      15
Unit-migration      15 57 61 111
Unit-migration, failure for octavians      114
van der Blij, F.      99 110
von Neumann, J.      143
Wigner, E. P.      143
Wondratschek, H.      48
Zassenhaus, H.      48
Zolotarev, G.      105

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