Classifying the absolute toral rank two case:
The problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p › 0 is a long standing one. Work on this question has been directed by the Kostrikin Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p › 5 a fi...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Berlin ; Boston
De Gruyter
[2017]
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| Ausgabe: | 2nd edition |
| Schriftenreihe: | De Gruyter expositions in mathematics
Volume 42 |
| Schlagworte: | |
| Online-Zugang: | FAB01 FAW01 FHA01 FHR01 FKE01 FLA01 TUM01 UBW01 UBY01 UPA01 FCO01 Volltext |
| Zusammenfassung: | The problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p › 0 is a long standing one. Work on this question has been directed by the Kostrikin Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p › 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p › 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p › 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every simple finite dimensional simple Lie algebra over an algebraically closed field of characteristic p › 3 is of classical, Cartan, or Melikian type. This is the second part of a three-volume book about the classifi cation of the simple Lie algebras over algebraically closed fi elds of characteristic › 3. The first volume contains the methods, examples and a first classification result. This second volume presents insight in the structure of tori of Hamiltonian and Melikian algebras. Based on sandwich element methods due to A. I. Kostrikin and A. A. Premet and the investigations of filtered and graded Lie algebras, a complete proof for the classification of absolute toral rank 2 simple Lie algebras over algebraically closed fields of characteristic › 3 is given. Contents Tori in Hamiltonian and Melikian algebras 1-sections Sandwich elements and rigid tori Towards graded algebras The toral rank 2 case |
| Beschreibung: | 1 Online-Ressource (viii, 382 Seiten) |
| ISBN: | 9783110517606 |
| DOI: | 10.1515/9783110517606 |
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| 490 | 1 | |a Simple Lie algebras over fields of positive characteristic / by Helmut Strade |v Volume 2 | |
| 490 | 1 | |a De Gruyter expositions in mathematics |v Volume 42 | |
| 520 | |a The problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p › 0 is a long standing one. Work on this question has been directed by the Kostrikin Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p › 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p › 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p › 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every simple finite dimensional simple Lie algebra over an algebraically closed field of characteristic p › 3 is of classical, Cartan, or Melikian type. This is the second part of a three-volume book about the classifi cation of the simple Lie algebras over algebraically closed fi elds of characteristic › 3. The first volume contains the methods, examples and a first classification result. This second volume presents insight in the structure of tori of Hamiltonian and Melikian algebras. Based on sandwich element methods due to A. I. Kostrikin and A. A. Premet and the investigations of filtered and graded Lie algebras, a complete proof for the classification of absolute toral rank 2 simple Lie algebras over algebraically closed fields of characteristic › 3 is given. Contents Tori in Hamiltonian and Melikian algebras 1-sections Sandwich elements and rigid tori Towards graded algebras The toral rank 2 case | ||
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Datensatz im Suchindex
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| id | DE-604.BV044343797 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:50:19Z |
| institution | BVB |
| isbn | 9783110517606 |
| language | English |
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| series2 | Simple Lie algebras over fields of positive characteristic / by Helmut Strade De Gruyter expositions in mathematics |
| spelling | Strade, Helmut 1942- Verfasser (DE-588)106816659 aut Classifying the absolute toral rank two case Helmut Strade 2nd edition Berlin ; Boston De Gruyter [2017] © 2017 1 Online-Ressource (viii, 382 Seiten) txt rdacontent c rdamedia cr rdacarrier Simple Lie algebras over fields of positive characteristic / by Helmut Strade Volume 2 De Gruyter expositions in mathematics Volume 42 The problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p › 0 is a long standing one. Work on this question has been directed by the Kostrikin Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p › 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p › 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p › 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every simple finite dimensional simple Lie algebra over an algebraically closed field of characteristic p › 3 is of classical, Cartan, or Melikian type. This is the second part of a three-volume book about the classifi cation of the simple Lie algebras over algebraically closed fi elds of characteristic › 3. The first volume contains the methods, examples and a first classification result. This second volume presents insight in the structure of tori of Hamiltonian and Melikian algebras. Based on sandwich element methods due to A. I. Kostrikin and A. A. Premet and the investigations of filtered and graded Lie algebras, a complete proof for the classification of absolute toral rank 2 simple Lie algebras over algebraically closed fields of characteristic › 3 is given. Contents Tori in Hamiltonian and Melikian algebras 1-sections Sandwich elements and rigid tori Towards graded algebras The toral rank 2 case Lie algebras, fields of positive characteristic, classification Erscheint auch als Druck-Ausgabe 978-3-11-051676-0 by Helmut Strade Simple Lie algebras over fields of positive characteristic Volume 2 (DE-604)BV035441977 2 De Gruyter expositions in mathematics Volume 42 (DE-604)BV004069300 42 https://doi.org/10.1515/9783110517606 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Strade, Helmut 1942- Classifying the absolute toral rank two case De Gruyter expositions in mathematics Lie algebras, fields of positive characteristic, classification |
| title | Classifying the absolute toral rank two case |
| title_auth | Classifying the absolute toral rank two case |
| title_exact_search | Classifying the absolute toral rank two case |
| title_full | Classifying the absolute toral rank two case Helmut Strade |
| title_fullStr | Classifying the absolute toral rank two case Helmut Strade |
| title_full_unstemmed | Classifying the absolute toral rank two case Helmut Strade |
| title_short | Classifying the absolute toral rank two case |
| title_sort | classifying the absolute toral rank two case |
| topic | Lie algebras, fields of positive characteristic, classification |
| topic_facet | Lie algebras, fields of positive characteristic, classification |
| url | https://doi.org/10.1515/9783110517606 |
| volume_link | (DE-604)BV035441977 (DE-604)BV004069300 |
| work_keys_str_mv | AT stradehelmut classifyingtheabsolutetoralranktwocase |