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Jacobson N. — Structure and Representations of Jordan Algebras
Jacobson N. — Structure and Representations of Jordan Algebras

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Название: Structure and Representations of Jordan Algebras

Автор: Jacobson N.

Язык: en

Рубрика: Математика/Алгебра/Абстрактная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1968

Количество страниц: 453

Добавлена в каталог: 19.03.2005

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