Albert algebras over commutative rings the last frontier of Jordan systems
Albert algebras provide key tools for understanding exceptional groups and related structures such as symmetric spaces. This self-contained book provides the first comprehensive reference on Albert algebras over fields without any restrictions on the characteristic of the field. As well as covering...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Cambridge, United Kingdom ; New York, NY
Cambridge University Press
2024
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| Schriftenreihe: | New mathematical monographs
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| Online-Zugang: | DE-12 DE-634 DE-92 URL des Erstveröffentlichers |
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| 100 | 1 | |a Garibaldi, Skip |d 1972- |0 (DE-588)138606889 |4 aut | |
| 245 | 1 | 0 | |a Albert algebras over commutative rings |b the last frontier of Jordan systems |c Skip Garibaldi, Holger P. Petersson, Michel L. Racine |
| 264 | 1 | |a Cambridge, United Kingdom ; New York, NY |b Cambridge University Press |c 2024 | |
| 300 | |a 1 Online-Ressource (xxii, 655 Seiten) | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a New mathematical monographs | |
| 500 | |a Title from publisher's bibliographic system (viewed on 07 Nov 2024) | ||
| 500 | |a Notation and conventions -- Prologue: the ancient protagonists -- The Graves-Cayley octonions -- Cartan-Schouten bases -- Unital subalgebras of O and their Z-structures | ||
| 520 | |a Albert algebras provide key tools for understanding exceptional groups and related structures such as symmetric spaces. This self-contained book provides the first comprehensive reference on Albert algebras over fields without any restrictions on the characteristic of the field. As well as covering results in characteristic 2 and 3, many results are proven for Albert algebras over an arbitrary commutative ring, showing that they hold in this greater generality. The book extensively covers requisite knowledge, such as non-associative algebras over commutative rings, scalar extensions, projective modules, alternative algebras, and composition algebras over commutative rings, with a special focus on octonion algebras. It then goes into Jordan algebras, Lie algebras, and group schemes, providing exercises so readers can apply concepts. This centralized resource illuminates the interplay between results that use only the structure of Albert algebras and those that employ theorems about group schemes, and is ideal for mathematics and physics researchers | ||
| 650 | 4 | |a Commutative rings | |
| 650 | 4 | |a Jordan algebras | |
| 700 | 1 | |a Petersson, Holger |d 1939- |0 (DE-588)140331247 |4 aut | |
| 700 | 1 | |a Racine, Michel L. |d 1945- |0 (DE-588)17234235X |4 aut | |
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Datensatz im Suchindex
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| author | Garibaldi, Skip 1972- Petersson, Holger 1939- Racine, Michel L. 1945- |
| author_GND | (DE-588)138606889 (DE-588)140331247 (DE-588)17234235X |
| author_facet | Garibaldi, Skip 1972- Petersson, Holger 1939- Racine, Michel L. 1945- |
| author_role | aut aut aut |
| author_sort | Garibaldi, Skip 1972- |
| author_variant | s g sg h p hp m l r ml mlr |
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| bvnumber | BV050111004 |
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| dewey-full | 512/.48 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.48 |
| dewey-search | 512/.48 |
| dewey-sort | 3512 248 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/9781009426862 |
| format | Electronic eBook |
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| id | DE-604.BV050111004 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-08T08:27:21Z |
| institution | BVB |
| isbn | 9781009426862 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035448005 |
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| owner | DE-12 DE-92 DE-634 |
| owner_facet | DE-12 DE-92 DE-634 |
| physical | 1 Online-Ressource (xxii, 655 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO BTU_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | New mathematical monographs |
| spelling | Garibaldi, Skip 1972- (DE-588)138606889 aut Albert algebras over commutative rings the last frontier of Jordan systems Skip Garibaldi, Holger P. Petersson, Michel L. Racine Cambridge, United Kingdom ; New York, NY Cambridge University Press 2024 1 Online-Ressource (xxii, 655 Seiten) txt rdacontent c rdamedia cr rdacarrier New mathematical monographs Title from publisher's bibliographic system (viewed on 07 Nov 2024) Notation and conventions -- Prologue: the ancient protagonists -- The Graves-Cayley octonions -- Cartan-Schouten bases -- Unital subalgebras of O and their Z-structures Albert algebras provide key tools for understanding exceptional groups and related structures such as symmetric spaces. This self-contained book provides the first comprehensive reference on Albert algebras over fields without any restrictions on the characteristic of the field. As well as covering results in characteristic 2 and 3, many results are proven for Albert algebras over an arbitrary commutative ring, showing that they hold in this greater generality. The book extensively covers requisite knowledge, such as non-associative algebras over commutative rings, scalar extensions, projective modules, alternative algebras, and composition algebras over commutative rings, with a special focus on octonion algebras. It then goes into Jordan algebras, Lie algebras, and group schemes, providing exercises so readers can apply concepts. This centralized resource illuminates the interplay between results that use only the structure of Albert algebras and those that employ theorems about group schemes, and is ideal for mathematics and physics researchers Commutative rings Jordan algebras Petersson, Holger 1939- (DE-588)140331247 aut Racine, Michel L. 1945- (DE-588)17234235X aut Erscheint auch als Druck-Ausgabe 9781009426855 https://doi.org/10.1017/9781009426862?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Garibaldi, Skip 1972- Petersson, Holger 1939- Racine, Michel L. 1945- Albert algebras over commutative rings the last frontier of Jordan systems Commutative rings Jordan algebras |
| title | Albert algebras over commutative rings the last frontier of Jordan systems |
| title_auth | Albert algebras over commutative rings the last frontier of Jordan systems |
| title_exact_search | Albert algebras over commutative rings the last frontier of Jordan systems |
| title_full | Albert algebras over commutative rings the last frontier of Jordan systems Skip Garibaldi, Holger P. Petersson, Michel L. Racine |
| title_fullStr | Albert algebras over commutative rings the last frontier of Jordan systems Skip Garibaldi, Holger P. Petersson, Michel L. Racine |
| title_full_unstemmed | Albert algebras over commutative rings the last frontier of Jordan systems Skip Garibaldi, Holger P. Petersson, Michel L. Racine |
| title_short | Albert algebras over commutative rings |
| title_sort | albert algebras over commutative rings the last frontier of jordan systems |
| title_sub | the last frontier of Jordan systems |
| topic | Commutative rings Jordan algebras |
| topic_facet | Commutative rings Jordan algebras |
| url | https://doi.org/10.1017/9781009426862?locatt=mode:legacy |
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