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Porteous I.R. — Clifford Algebras and the Classical Groups
Porteous I.R. — Clifford Algebras and the Classical Groups



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Название: Clifford Algebras and the Classical Groups

Автор: Porteous I.R.

Аннотация:

This book reflects the growing interest in the theory of Clifford algebras and their applications. The author has reworked his previous book on this subject, Topological Geometry, and has expanded and added material. As in the previous version, the author includes an exhaustive treatment of all the generalizations of the classical groups, as well as an excellent exposition of the classification of the conjugation anti-involution of the Clifford algebras and their complexifications. Toward the end of the book, the author introduces ideas from the theory of Lie groups and Lie algebras. This treatment of Clifford algebras will be welcomed by graduate students and researchers in algebra.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 295

Добавлена в каталог: 04.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute value of quaternion      60
Action, Clifford      257
Action, spinor      257
Adams, J.F.      x 186 187 285
Adjoint      27 53 96 101
Adjoint representation      238
Admissible chart      217
Affine form      112
Affine map      6
Affine space      6
Affine subspace      6 212
Ahlfors, L      167 176 254 285
Algebra anti-isomorphism      9
Algebra isomorphism      9
Algebra map      9
Algebra, alternative      179
Algebra, Cayley      ix 180
Algebra, Clifford      123
Algebra, division      178
Algebra, extensive      138
Algebra, exterior      138
Algebra, geometric      123
Algebra, Grassmann      138
Algebra, Jordan      257
Algebra, Lie      239 242
Algebra, linear      9
Algebra, Pauli      152
Algebra, tensor      124
Algebra-reversing map      9
Alternative algebra      179
Analytic      209
Angle, absolute      39
Angles, preservation of      245
Annihilator, dual      4
Annihilator, orthogonal      32
Anti-automorphism of H      62
Anti-automorphism, algebra      13
Anti-involution of H      64
Anti-involution, algebra      13
Anti-rotation      27 143
Arnol’d, V.I.      66 112 285
Artin, E.      x 176 285
Atiyah, M.F.      x 124 285
Atlas      215
Atlas, standard      111
Automorphism of H      62
Automorphism, algebra      13
Automorphism, linear      3 5
Automorphism, orthogonal      27
Automorphism, triality      267
Axis of rotation      35
Banach space      202
Basis      2
Basis theorem for ${}^2 K$-linear spaces      92
Basis theorem for hermitian spaces      54
Basis theorem for real quadratic spaces      34
Basis theorem for symmetric correlated quaternionic spaces      77
Benn, I.M.      166 285
Bijection      2
Bijective      2
Bilinear map      4
Biquaternions      174
Bivector      176
Bott, R.      124 186 187 285 287
Boudet, R.      x 287
Boundary point      192
bounded linear map      194
Boyer, R.H.      x
Brack, R.H.      186 188 285
Bracket, Lie      239
Brackx, F.      x 285
Bredon, G.E.      277 285
Bundle, tangent      219 220
Cartan, E.      247 256 278 285
Cauchy — Schwarz inequality      39
Cayley algebra, ix      180
Cayley chart      118 174
Cayley heptagon      185
Cayley numbers      165
Cayley projective line      187
Cayley projective plane      187
Cayley triangle      184
Cayley, A.      180 286
Centre      40
Centre of algebra      10
Chain rule      203 207
Chart      176 215
Chart, admissible      217
Chart, Cayley      118 174
Chart, Pfaffian      176
Chart, standard      111 215
Charts on quadric Grassmannians      114
Chevalley, C.      124 243 286
Chisholm, J.S.R.      x 286
Choice, axiom of      2
Circle group      56 57
Circle, unit      40
Classical group      100 103
Classification theorem for ${}^2 K$-correlations      98
Classification theorem for ${}^2 K$-semi-linear maps      94
Classification theorem for complex quadratic spaces      49
Classification theorem for complex symplectic spaces      50
Classification theorem for hermitian spaces      55
Classification theorem for real symplectic spaces      47
Classification theorem for symmetric correlated quaternionic spaces      78
Classification theorem of real quadratic spaces, first part      34
Classification theorem of real quadratic spaces, second part      36
Clifford action      257
Clifford algebra, complex      134
Clifford algebra, even      136
Clifford algebra, real      123
Clifford embedding      262
Clifford group      141
Clifford homogeneous space      262
Clifford matrix      167
Clifford, W.K.      123 286
Closed map      196
Closed set      192
Cnops, J.      164 167 168 172 255 286
Code numbers for ten types of classical group      103
Code numbers for ten types of matrix algebra with anti-involution      155
Coimage      1
Common, A.K.      x 286
Commutative diagram      19
Compact space      198
Compactification, conformal      247
Compactification, projective      246
companion      267
Companion involution      266
Complement, linear      3
Complement, orthogonal      32
Complex field, as real algebra      9
Complex group = symplectic group      79
Complex orthogonal group      50
Complex quadratic space      49
Complex Stiefel manifold      265
Complex symplectic plane      50
Complex symplectic space      50
Complexification      86 105
Composite      1
Conformal compactification      247
Conformal group      248
Conformal map      245
Conformal spheres      248
Conformal transformation, special      252
Conjugate of a quaternion      59
Conjugation      135 148
Conjugation anti-involution      59
Connected      199
Continuous map      193
Continuously differentiable map      205
contour      1
Contraction Lemma      211
Correlated ${}^2 K$-space      95
Correlated linear space      24
Correlated quaternionic space      74
Correlation      52 74
Correlation, linear      24
Correlation, semi-linear      95
Correlation, symmetric      24
Coset space representation      20
Cover, double      146
Cover, induced      197
Cover, open      197
Cross product      60
Decomposition, orthogonal      32
Decomposition, Witt      37 109
Delanghe, R.      viii 285
Determinant      6 98
Determinant, absolute      70
Diagram chasing      18
Diffeomorphism      211 218
Differentiable map      205
Differential of a map      205
Differential, higher-order      209
DIMENSION      2
Dimension of affine subspace      212
Dimension of classical group      103
Dimension of Grassmannian      111
Dimension of smooth manifold      217
Dimension of submanifold      212
Dimension, quaternionic      68
Dirac spinors      165
Direct product      3
Direct sum      3
Disconnected      199
Dissimilar      14
Distance      39 192
Division algebra      178
Division algebra, normed      179
Domain      1
Double cover      146
Double field      5 91
Double field ${}^2 K$, as real algebra      9
Dual      52
Dual annihilator      4
Dual linear map      4
Dual linear space      4
Dual of semi-linear map      73 95
Dual, linear      68
Elstrodt, J.      167 255 286
Embedding      196 213
Embedding, Clifford      262
Endomorphism, linear      5
Epstein, D.B.A.      264 276 288
Equation of map      2
Equivalent atlases      216
Equivalent correlations      52
Equivalent norms      194
Equivalent semi-linear correlations      74 95
Equivalent smooth manifolds      217
Euclidean space      39
Euclidean, locally      215
Even Clifford algebra      136
Exact pair      18
Exact sequence      18
Exact sequence, short      18
Exact, left-coset      20 108
Existence theorem for Clifford algebras      131
Extensive algebra      138
Exterior algebra      138
Fibre      1 212
Field      2
Field, complex      2
Field, double      5 91
Field, real      2
Fillmore, J.      167 255 286
Finite-dimensional      2
Five      154
Form induced by correlation      74
Form, Hermitian      52
Form, quadratic      22
Form, sesqui-linear      95
Free, linearly      92
Freudenthal, H.      278 286
Freudenthal’s principle of triality      278
Frobenius, G.      186
Fuchs, L.      13 286
General linear group      7 98
General linear group, thought of as a unitary group      91
Generators, set of      12
Geometric algebra      123
Gilmore, R.      243 277 286
Grade involution      135
Gradient norm      194
Grassmann algebra      138
Grassmann, H.      138 286
Grassmannian      110
Grassmannian, quadric      112
Grassmannians as coset spaces      113
Graves, J.      180 286
Group $G_2$      ix 270
Group action      21
Group action, Lie      233
Group map = group homomorphism      20
Group map, Lie      231
Group map, topological      225
Group, circle      56 57
Group, classical      100 103
Group, Clifford      141
Group, complex orthogonal      50
Group, conformal      248
Group, general linear      7 98
Group, Lie      viii 100 103 231
Group, linear      7
Group, Lipschitz      141
Group, Lorentz      238
Group, Moebius      248 255
Group, orthogonal      27
Group, Pin      146
Group, quaternionic      78
Group, real symplectic      47
Group, special linear      7 99
Group, special unitary      55
Group, spin      146
Group, topological      225
Group, unitary      55 104
Grunewald, F.      167 255 286
Haantjes, J.      246 286
Half-spinor space      134
Hamilton triangle      183
Hamilton, Sir W.R.      58 286
Hampson, A.      ix 286
Hausdorff space      192
Heine — Borel theorem      197
Helgason, S.      243 277 286
Helmstetter, J.      x 287
Heptagon, Cayley      185
Hermann, R.      247 286
Hermitian form      52
Hermitian product      52
Hermitian space      52
Higher-order differential      209
Homeomorphism      193
Homogeneous space      226
Homogeneous space, Clifford      262
Hopf map      111 258 259
Hopf, H.      122 286
Hurwitz pair      164
Hurwitz, A.      164 165 186 286
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