Structure and representations of Jordan algebras:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
1968
|
| Series: | Colloquium publications / American Mathematical Society
39 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 453 S. |
Staff View
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| 245 | 1 | 0 | |a Structure and representations of Jordan algebras |c by Nathan Jacobson |
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| 300 | |a X, 453 S. | ||
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Record in the Search Index
| _version_ | 1804117260833390592 |
|---|---|
| adam_text | TABLE OF CONTENTS
Chapter I. Foundations j
1. Special Jordan algebras and Jordan algebras 3
2. Free special Jordan algebras. Cohn s theorem 6
3. Homomorphic images of special Jordan algebras 10
4. Some constructions of Jordan algebras 12
5. Alternative algebras and Jordan algebras 15
6. Varieties of algebras. Free algebras 23
7. Basic Jordan identities. Jordan triple product 33
8. Strongly associative subalgebras. Jordan triple
product identities 37
9. Macdonald s theorem. Shirshov s theorem 40
10. ^ identities. Exceptional character of §(O)3 49
11. Inverses and zero divisors 51
12. Homotopy and isotopy 56
Chapter II. Elements of representation theory 63
1. Associative specializations and universal
envelopes 65
2. Special universal envelopes for Jordan algebras
with 1 and for direct sums 72
3. Examples 74
4. Associative algebras with involutions and Jordan
algebras 76
5. Bimodules for algebras in a variety ~r(I) 79
6. Birepresentations for an algebra in a variety y (/) 82
7. Multiplication specializations and universal
envelopes 86
8. Extension of algebras and factor sets 91
9. Jordan bimodules and universal multiplication
envelopes 95
10. Associative specializations and multiplicative
specializations 99
11. Universal multiplication envelopes for Jordan
algebras with identity elements 102
vii
12. Some basic criteria 106
13. Examples and applications 110
Chapter III. Peirce decompositions and Jordan matrix
ALGEBRAS 117
1. Peirce decompositions 118
2. Jordan matrix algebras 125
3. Coordinatization theorems 132
4. Perfection of certain classes of associative algebras
with involutions 138
5. Unital bimodules for Jordan matrix algebras 144
6. Some remarks on the universal envelopes of Jordan
matrix algebras 147
7. Lifting of idempotents and Jordan matrix
algebras 148
Chapter IV. Jordan algebras with minimum conditions on
QUADRATIC IDEALS 152
1. Quadratic ideals 153
2. Axioms and first structure theorem 157
3. Determination of a class of alternative algebras with
involution 162
4. Simple Jordan algebras of capacity two 171
5. Second structure theorem 178
6. Special universal envelopes. Isomorphisms and
derivations of special simple Jordan algebras
satisfying the axioms 183
7. Alternative set of axioms 187
Chapter V. Structure theory for finite dimensional Jordan
ALGEBRAS 189
1. Ideals and associator ideals 190
2. Solvable ideals 192
3. Finite dimensional nil algebras 195
4. Reduced Jordan algebras 197
5. Structure of finite dimensional semisimple Jordan
algebras 200
6. Reduced simple Jordan algebras 202
7. Finite dimensional central simple Jordan algebras 206
viii
Chapter Vf. Generic minimum polynomials, traces and norms ... 213
1. Differentiation of rational expressions 214
2 Differential calculus of rational mappings 215
3 Generic minimum polynomial of a strictly power
associative algebra 221
4. Some important examples 229
5. Multiplicative properties of the generic norm 234
6. Separable algebras 238
7. Norm similarity of Jordan algebras. The group of
norm preserving linear transformations 241
8. Determination of M(3) for 3 special central simple
of degree ^3 247
9. The Lie algebras 3JK3), 9fto(3) and Der3 for 3
separable 253
Chapter VII. Representation theory for separable Jordan algebras 259
1. Structure of Clifford algebras 260
2. Structure of meson algebras 264
3. Universal envelopes for finite dimensional special
central simple Jordan algebras of degree ^ 3 272
4. Bimodules for composition algebras and reduced
Jordan algebras 277
5. Separability of 3 and UQ) 286
6. The theorem of Albert Penico Taft 286
7. Derivations into bimodules 292
8. Uniqueness of the Albert Penico Taft decom¬
position 303
Chapter VIII. Connections with lie algebras 307
1. Associator structure of a Jordan algebra. Abstract
Lie triple systems 307
2. Some results on completely reducible Lie algebras
of linear transformations with applications to Jordan
algebras 312
3. Operator commutativity 320
4. Derivations of semisimple Jordan algebras of
characteristic 0 into bimodules 323
5. The Tits Koecher construction of a Lie algebra from
a Jordan algebra 324
6. Subalgebras and ideals of 5* = #(3) 329
is
7. Application to a proof of the Albert Penico
Theorem 333
8. Associative bilinear forms 336
9. Examples. Functorial constructions 339
10. Associator nilpotent Jordan algebras 343
11. Cartan subalgebras of Jordan algebras. Associator
regular elements 349
12. Application to generic traces 352
13. Conjugacy of Cartan subalgebras 353
Chapter IX. Exceptional Jordan algebras 356
1. Preliminaries on identities and subalgebras 357
2. Elements of rank one. Uniqueness of the coefficient
algebra 364
3. Aut 3/Ote 370
4. Conditions for isomorphism 378
5. More on Aut 3 382
6. Invariant factor theorem for split 3 389
7. Moufang projective planes 393
8. Elations 397
9. Harmonicity 402
10. Fundamental theorem of projective geometry for the
planes ^5(3) 404
11. Connections with exceptional Lie algebras 407
12. Exceptional Jordan division algebras 412
Further results and open questions 423
Bibliography 443
Subject index 451
z
|
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| dewey-full | 512/.8 |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.8 |
| dewey-search | 512/.8 |
| dewey-sort | 3512 18 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:51:35Z |
| institution | BVB |
| language | English |
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| physical | X, 453 S. |
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| publishDate | 1968 |
| publishDateSearch | 1968 |
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| publisher | American Math. Soc. |
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| series2 | Colloquium publications / American Mathematical Society |
| spelling | Jacobson, Nathan 1910-1999 Verfasser (DE-588)119081873 aut Structure and representations of Jordan algebras by Nathan Jacobson Providence, RI American Math. Soc. 1968 X, 453 S. txt rdacontent n rdamedia nc rdacarrier Colloquium publications / American Mathematical Society 39 Algebra Nao Associativa larpcal Algebra larpcal Jordan, Algèbres de Jordan algebras Jordan-Algebra (DE-588)4162770-2 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 gnd rswk-swf Jordan-Algebra (DE-588)4162770-2 s DE-604 Darstellung Mathematik (DE-588)4128289-9 s American Mathematical Society Colloquium publications 39 (DE-604)BV035417609 39 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001859303&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jacobson, Nathan 1910-1999 Structure and representations of Jordan algebras Algebra Nao Associativa larpcal Algebra larpcal Jordan, Algèbres de Jordan algebras Jordan-Algebra (DE-588)4162770-2 gnd Darstellung Mathematik (DE-588)4128289-9 gnd |
| subject_GND | (DE-588)4162770-2 (DE-588)4128289-9 |
| title | Structure and representations of Jordan algebras |
| title_auth | Structure and representations of Jordan algebras |
| title_exact_search | Structure and representations of Jordan algebras |
| title_full | Structure and representations of Jordan algebras by Nathan Jacobson |
| title_fullStr | Structure and representations of Jordan algebras by Nathan Jacobson |
| title_full_unstemmed | Structure and representations of Jordan algebras by Nathan Jacobson |
| title_short | Structure and representations of Jordan algebras |
| title_sort | structure and representations of jordan algebras |
| topic | Algebra Nao Associativa larpcal Algebra larpcal Jordan, Algèbres de Jordan algebras Jordan-Algebra (DE-588)4162770-2 gnd Darstellung Mathematik (DE-588)4128289-9 gnd |
| topic_facet | Algebra Nao Associativa Algebra Jordan, Algèbres de Jordan algebras Jordan-Algebra Darstellung Mathematik |
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