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| Jacobson N. — Structure and Representations of Jordan Algebras |
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Albert — Jacobson theorem 369
Albert — Jacobson — McCrimmon theorem 198
Albert — Paige theorem 50
Albert — Penico-Taft factor 303
Albert — Penico-Taft theorem 417 421
Albert's theorem on nil Jordan algebras 196
Albert's theorem on semisimple Jordan algebras 201
Albert's theorem on simple Jordan algebras 204
Albert's theorem on solvable Jordan algebras 195
Algebra composition 162
Algebra of octonions 17
Algebra with involutions 208
Algebra with involutions, center of 208
Algebra with involutions, central simple 208
Algebra with involutions, centroid of 207
Algebra with involutions, degree of 209
Algebra with involutions, derivation of 144
Algebra with involutions, homomorphism of an 13
Algebra with involutions, ideal of 128
Algebra with involutions, multiplication algebra of 207
Algebra with involutions, perfect 76
Algebra with involutions, simple Artinian 178
Algebra with involutions, subalgebra of 128
Algebra, alternative 15
Algebra, alternative division 169
Algebra, Cayley 17
Algebra, Clifford 75
Algebra, degree of an 222
Algebra, exterior 74
Algebra, free I- 26
Algebra, Lie 4
Algebra, Malcev 33
Algebra, meson 115
Algebra, nil 195
Algebra, opposite 13
Algebra, simple 60
Algebra, strongly special 101
Algebra, unramified 229
Algebraic Jordan algebras 54
Alternative algebra 15
Alternative bimodule 80
Alternative division algebra 169
Associates 318
Associative 199
Associative, algebra with involution 13
Associative, specialization 63
Associator 15
Associator, ideal 190
Associator, nilpotent element 346
Associator, regular element 351
Basic Jordan identities 33
Bimodule 80
Bimodule with involution 145
Bimodule with involution, alternative 145
Bimodule with involution, associative 145
Birepresentation 84
Birepresentation, regular 90
Capacity 158
Car tan subalgebra 350
Cayley algebra 17
Cayley bimodule with involution 279
Cayley bimodule with involution, center 18
Center of algebra with involution 208
Central 206
Central, simple algebra with involution 208
Centroid 206
Centroid of algebra with involution 207
Chain rule 215
Clifford algebra 75
Clifford group 371
Clifford groupeven (or second) 372
Collineation 379
Composition algebra 162
Conn's theorem 8
Coordinization Theorem 137
Correlation 397
Degree 209
Degree of an algebra 223
Degree of the algebra with involution 209
Derivation 35
Derivation into bimodule 292
Derivation of an algebra with involution 144
Derived elements 84
Differential 217 218
Direct limit 69
Directional derivative 214 216
Elation 397
Elementary semisimple Jordan algebra 318
Elements of rank one 364
Euler's differential equation 219
Exceptional Jordan algebra 6 11
Exchange automorphism 101
Extension 91
Exterior algebra 74
Factor set 93
First Structure Theorem 161
Formally real 205
Free associative algebra 25
Free I-algebra 26
Free Jordan algebra 40
Free monad 24
Free monoid 23 24
Free nonassociative algebra 25
Free special Jordan algebra 7
Generic element 222
Generic minimum polynomial 223
Generic norm 223
Generic trace 223
Glennie's theorem 51
Harris' theorem 293 410
Homogeneous rational mapping 219
Homomorphism of an algebra with involution 13
Homotope 56
Homotopy 57
Hua's identity 2 54
Ideal of algebra with involution 128
Inner automorphism 60
Inner automorphism of associative algebra with involution 248
Inner derivation 35
Inner derivation into bimodule 292
Inner norm preserving group 246
Inner structure group 59
Invariant 220
Inverse 52
Invertible 52
Involution of orthogonal type 341
Involution of symplectic type 285
Involution of the first kind 208
Involution of the second kind 208
Involution, canonical 125
Involution, standard 19 125
Isotope 56
Isotopic 57
Isotopy 57
Jacobson and Richart theorem 2
Jacobson's theorem 369 401
Jordan algebra 6
| Jordan algebra of a symmetric bilinear form 14
Jordan algebra, elementary semisimple 318
Jordan algebra, exceptional 6 11
Jordan algebra, free 40
Jordan algebra, free special 7
Jordan algebra, noncommutative 33
Jordan algebra, nondegenerate 155
Jordan algebra, purely inseparable 344
Jordan algebra, reduced 197
Jordan algebra, reflexive 76
Jordan algebra, regular 55
Jordan algebra, special 3 4 6
Jordan algebra, split 204
Jordan bimodule 80
Jordan division algebra 53
Jordan element 7
Jordan homomorphism 2
Jordan integral domain 53
Jordan matrix algebra 127
Jordan product 3
Jordan triple product 36
Jordan, von Neumann and Wigner theorem 205
Left free cyclic bimodule 279
Lie algebra 4
Lie element 9
Lie invariant 220
Lie product 4
Lie semi-invariant 220
Lie triple system of linear transformations 35
Lie triple system, derivation of 308
Lie triple system, derivation of, inner 309
Lie triple system, ideal in a 311
Lie triple system, standard Lie envelope of a 310
Lie triple system, universal Lie envelope of a 310
Linear property 78
Linearization 28
Little projective group 398
Macdonald's theorem 41
Main involution 65
Malcev algebra 33
Martinaale theorem 141
Meson algebra 115
Monad (monoid) 23
Moufang's identities 15
Multiplication algebra 206
Multiplication algebraof algebra with involution 207
Multiplication specialization 63 86
Nil algebra 195
Nilpotent 195
Nncommutative Jordan algebra 33
Nonassociative algebra 1
Nondegenerate Jordan algebra 155
Norm, class 379
Norm, preserving group 241
Norm, semisimilarity 394
Norm, similarity 394
Nucleus 18
Null extension 91
Octonions 16
Operator commutativity 310
Opposite algebra 13
Orthogonal idempotents, connected 122
Orthogonal idempotents, strongly 122
Osborn's theorem 176
Peirce decomposition 118 120
Peirce decomposition of alternative algebras 165
Peirce decomposition, formulas (PD) 121
Penico sequence 192
Penico solvable 332
Perfect associative algebra with involution 76
Pfaffian 231
Polynomial functions 215
Polynomial mapping 218
Power associative 36
Power associativity 5
Primitive idempotents, absolutely 197
Primitive idempotents, completely 158
Projective transformation 397
Purely inseparable Jordan algebra 344
Quadratic ideal 153
Quadratic ideal, maximal 157
Quadratic ideal, minimal 154
Quadratic ideal, minimal conditions for 157
Quadratic ideal, principal 154
Quasi-inverse 55
Radical 192
Rational function 216
Rational mappings 217
Reduced, Jordan algebra 197
Reduced, orthogonal groups 372
Reducing set of idempotents 197
Reflexive Jordan algebra 55
Regular bimodule 81
Regular bimodule with involution 278
Regular birepresentation 90
Regular Jordan algebra 55
Reversal operation 8
s-identity 49
Schafer's theorem 346
Second Structure Theorem 179
Semi-invariant 220
Semiderivation 185
Semisimple 192
Separable 238
Shirshov — Cohn theorem 48
Shirshov's theorem 47
Simple algebra 60
Simple Artinian algebra with involution 178
Simple components 162
Solvable ideals 192
Special Jordan algebra 3 4 6
Special universal envelope 65
Special universal envelope, construction of a 68
Special universal envelope, squared 100
Special universal envelope, unital 73
Special universal envelope, unital squared 104
Special universal functor 69
Spin group 372
Spinorial norm 372
Split Jordan algebra 204
Split null extension 80
Springer's theorem 378 381 406
Strictly power associative 222
Strongly associative algebra 38
Strongly special algebra 101
Structure group 59
Subalgebra of algebra with involution 128
Taft's theorem 336
Type of an involution 209
Universal I-multiplication envelope 103
Universal multiplication 95
Universal multiplication, functor 90
Universal unital multiplication envelope 103
Unramified algebra 229
Variety 25
Zero divisor 53
Zero divisor, absolute 154
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