Graded simple Jordan superalgebras of growth one:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
2001
|
| Series: | American Mathematical Society: Memoirs of the American Mathematical Society
711 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 150, number 711 (second of 5 numbers)." |
| Physical Description: | IX, 140 S. |
| ISBN: | 082182645X |
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MARC
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| 100 | 1 | |a Kac, Victor G. |d 1943- |e Verfasser |0 (DE-588)110066820 |4 aut | |
| 245 | 1 | 0 | |a Graded simple Jordan superalgebras of growth one |c V. G. Kac ; C. Martinez ; E. Zelmanov |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c 2001 | |
| 300 | |a IX, 140 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a American Mathematical Society: Memoirs of the American Mathematical Society |v 711 | |
| 500 | |a "Volume 150, number 711 (second of 5 numbers)." | ||
| 650 | 7 | |a Jordan-algebra's |2 gtt | |
| 650 | 7 | |a Superalgebra's |2 gtt | |
| 650 | 4 | |a Jordan algebras | |
| 650 | 4 | |a Superalgebras | |
| 650 | 0 | 7 | |a Superalgebra |0 (DE-588)4304028-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Jordan-Algebra |0 (DE-588)4162770-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Jordan-Algebra |0 (DE-588)4162770-2 |D s |
| 689 | 0 | 1 | |a Superalgebra |0 (DE-588)4304028-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Martinez, Consuelo |d 1955- |e Verfasser |0 (DE-588)1146310722 |4 aut | |
| 700 | 1 | |a Zelmanov, Efim |d 1955- |e Verfasser |0 (DE-588)1146310730 |4 aut | |
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Record in the Search Index
| _version_ | 1804128463256289280 |
|---|---|
| adam_text | Contents
Introduction 1
Statement of the Problem 1
Definitions and Notation 2
The Main Result 3
Structure of the Proof 6
Chapter 1. Structure of the Even Part 9
1.1. General results 9
Chapter 2. Cartan type 33
2.1. Results 33
2.2. A/I one sided graded 33
Chapter 3. Even Part is Direct Sum of two Loop Algebras 37
3.1. General Results 37
3.2. A = F[t n,tn] 40
3.3. A = F[tini,t^l]®F[t^n2,t^2} 48
3.4. A = C{G ) © £{G) 55
Chapter 4. A is a Loop Algebra 59
4.1. General Results 59
Chapter 5. J is a finite dimensional Jordan Superalgebra or a Jordan Superalgebra
of a Superform 69
5.1. A is finite dimensional 69
5.2. A/I finite dimensional, / ^ (0) 71
5.3. A is a Jordan algebra of a bilinear form 73
Chapter 6. The Main Case 75
6.1. Splitting Theorem 75
6.2. Structure of J 89
Chapter 7. Impossible Cases 127
7.1. / = (0), A = Aw 0 A{2); A^I is a loop algebra, A 2 is one sided
graded 127
7.2. A = A^ ®A 2 A^ is a negatively graded algebra, A(2) is a positively
graded algebra 128
7.3. A = A^ ffi A^ with A^ infinite dimensional Jordan algebra of a
bilinear form 129
vii
viii CONTENTS
7.4. I 7^ (0), yl/J is an infinite dimensional Jordan algebra of a nondegenerate
symmetric bilinear form 131
7.5. A = A(1) 0 v4(2), A^ is finite dimensional; A(2 is a loop algebra 133
Bibliography 139
|
| any_adam_object | 1 |
| author | Kac, Victor G. 1943- Martinez, Consuelo 1955- Zelmanov, Efim 1955- |
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| author_facet | Kac, Victor G. 1943- Martinez, Consuelo 1955- Zelmanov, Efim 1955- |
| author_role | aut aut aut |
| author_sort | Kac, Victor G. 1943- |
| author_variant | v g k vg vgk c m cm e z ez |
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| classification_rvk | SI 130 |
| classification_tum | MAT 176f |
| ctrlnum | (OCoLC)45320593 (DE-599)BVBBV013652587 |
| dewey-full | 510 512/.24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 512 - Algebra |
| dewey-raw | 510 512/.24 |
| dewey-search | 510 512/.24 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV013652587 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:49:38Z |
| institution | BVB |
| isbn | 082182645X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009328300 |
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| physical | IX, 140 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spelling | Kac, Victor G. 1943- Verfasser (DE-588)110066820 aut Graded simple Jordan superalgebras of growth one V. G. Kac ; C. Martinez ; E. Zelmanov Providence, Rhode Island American Mathematical Society 2001 IX, 140 S. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Memoirs of the American Mathematical Society 711 "Volume 150, number 711 (second of 5 numbers)." Jordan-algebra's gtt Superalgebra's gtt Jordan algebras Superalgebras Superalgebra (DE-588)4304028-7 gnd rswk-swf Jordan-Algebra (DE-588)4162770-2 gnd rswk-swf Jordan-Algebra (DE-588)4162770-2 s Superalgebra (DE-588)4304028-7 s DE-604 Martinez, Consuelo 1955- Verfasser (DE-588)1146310722 aut Zelmanov, Efim 1955- Verfasser (DE-588)1146310730 aut American Mathematical Society: Memoirs of the American Mathematical Society 711 (DE-604)BV008000141 711 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009328300&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kac, Victor G. 1943- Martinez, Consuelo 1955- Zelmanov, Efim 1955- Graded simple Jordan superalgebras of growth one American Mathematical Society: Memoirs of the American Mathematical Society Jordan-algebra's gtt Superalgebra's gtt Jordan algebras Superalgebras Superalgebra (DE-588)4304028-7 gnd Jordan-Algebra (DE-588)4162770-2 gnd |
| subject_GND | (DE-588)4304028-7 (DE-588)4162770-2 |
| title | Graded simple Jordan superalgebras of growth one |
| title_auth | Graded simple Jordan superalgebras of growth one |
| title_exact_search | Graded simple Jordan superalgebras of growth one |
| title_full | Graded simple Jordan superalgebras of growth one V. G. Kac ; C. Martinez ; E. Zelmanov |
| title_fullStr | Graded simple Jordan superalgebras of growth one V. G. Kac ; C. Martinez ; E. Zelmanov |
| title_full_unstemmed | Graded simple Jordan superalgebras of growth one V. G. Kac ; C. Martinez ; E. Zelmanov |
| title_short | Graded simple Jordan superalgebras of growth one |
| title_sort | graded simple jordan superalgebras of growth one |
| topic | Jordan-algebra's gtt Superalgebra's gtt Jordan algebras Superalgebras Superalgebra (DE-588)4304028-7 gnd Jordan-Algebra (DE-588)4162770-2 gnd |
| topic_facet | Jordan-algebra's Superalgebra's Jordan algebras Superalgebras Superalgebra Jordan-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009328300&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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