Simple Lie Algebras over Fields of Positive Characteristic - Structure Theory:
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 |
| Veröffentlicht: |
Berlin
De Gruyter
2017
|
| Ausgabe: | 2nd ed. |
| Schriftenreihe: | De Gruyter Expositions in Mathematics
38 |
| 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. In the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic. This first volume is devoted to preparing the ground for the classification work to be performed in the second and third volumes. The concise presentation of the general theory underlying the subject matter and the presentation of classification results on a subclass of the simple Lie algebras for all odd primes will make this volume an invaluable source and reference for all research mathematicians and advanced graduate students in algebra. The second edition is corrected. Contents Toral subalgebras in p-envelopes Lie algebras of special derivations Derivation simple algebras and modules Simple Lie algebras Recognition theorems The isomorphism problem Structure of simple Lie algebras Pairings of induced modules Toral rank 1 Lie algebras |
| Beschreibung: | 1 Online-Ressource (viii, 540 Seiten) 2 Illustrationen |
| ISBN: | 9783110515442 |
| DOI: | 10.1515/9783110515442 |
Internformat
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| 490 | 1 | |a Simple Lie Algebras over Fields of Positive Characteristic / by Helmut Strade |v Volume 1 | |
| 490 | 1 | |a De Gruyter Expositions in Mathematics |v 38 | |
| 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. In the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic. This first volume is devoted to preparing the ground for the classification work to be performed in the second and third volumes. The concise presentation of the general theory underlying the subject matter and the presentation of classification results on a subclass of the simple Lie algebras for all odd primes will make this volume an invaluable source and reference for all research mathematicians and advanced graduate students in algebra. The second edition is corrected. Contents Toral subalgebras in p-envelopes Lie algebras of special derivations Derivation simple algebras and modules Simple Lie algebras Recognition theorems The isomorphism problem Structure of simple Lie algebras Pairings of induced modules Toral rank 1 Lie algebras | ||
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Datensatz im Suchindex
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| author | Strade, Helmut 1942- |
| author_GND | (DE-588)106816659 |
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| author_sort | Strade, Helmut 1942- |
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| dewey-full | 510 |
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| dewey-ones | 510 - Mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9783110515442 |
| edition | 2nd ed. |
| format | Electronic eBook |
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| publishDate | 2017 |
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| series | De Gruyter Expositions in Mathematics |
| 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 Simple Lie Algebras over Fields of Positive Characteristic - Structure Theory Helmut Strade 2nd ed. Berlin De Gruyter 2017 1 Online-Ressource (viii, 540 Seiten) 2 Illustrationen txt rdacontent c rdamedia cr rdacarrier Simple Lie Algebras over Fields of Positive Characteristic / by Helmut Strade Volume 1 De Gruyter Expositions in Mathematics 38 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. In the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic. This first volume is devoted to preparing the ground for the classification work to be performed in the second and third volumes. The concise presentation of the general theory underlying the subject matter and the presentation of classification results on a subclass of the simple Lie algebras for all odd primes will make this volume an invaluable source and reference for all research mathematicians and advanced graduate students in algebra. The second edition is corrected. Contents Toral subalgebras in p-envelopes Lie algebras of special derivations Derivation simple algebras and modules Simple Lie algebras Recognition theorems The isomorphism problem Structure of simple Lie algebras Pairings of induced modules Toral rank 1 Lie algebras Strukturtheorie (DE-588)4126908-1 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie algebras, fields of positive characteristic, structure theory Lie-Algebra (DE-588)4130355-6 s Strukturtheorie (DE-588)4126908-1 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Druck-Ausgabe 978-3-11-051516-9 by Helmut Strade Simple Lie Algebras over Fields of Positive Characteristic Volume 1 (DE-604)BV035441977 1 De Gruyter Expositions in Mathematics 38 (DE-604)BV004069300 38 https://doi.org/10.1515/9783110515442 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Strade, Helmut 1942- Simple Lie Algebras over Fields of Positive Characteristic - Structure Theory De Gruyter Expositions in Mathematics Strukturtheorie (DE-588)4126908-1 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4126908-1 (DE-588)4130355-6 |
| title | Simple Lie Algebras over Fields of Positive Characteristic - Structure Theory |
| title_auth | Simple Lie Algebras over Fields of Positive Characteristic - Structure Theory |
| title_exact_search | Simple Lie Algebras over Fields of Positive Characteristic - Structure Theory |
| title_full | Simple Lie Algebras over Fields of Positive Characteristic - Structure Theory Helmut Strade |
| title_fullStr | Simple Lie Algebras over Fields of Positive Characteristic - Structure Theory Helmut Strade |
| title_full_unstemmed | Simple Lie Algebras over Fields of Positive Characteristic - Structure Theory Helmut Strade |
| title_short | Simple Lie Algebras over Fields of Positive Characteristic - Structure Theory |
| title_sort | simple lie algebras over fields of positive characteristic structure theory |
| topic | Strukturtheorie (DE-588)4126908-1 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Strukturtheorie Lie-Algebra |
| url | https://doi.org/10.1515/9783110515442 |
| volume_link | (DE-604)BV035441977 (DE-604)BV004069300 |
| work_keys_str_mv | AT stradehelmut simpleliealgebrasoverfieldsofpositivecharacteristicstructuretheory AT walterdegruytergmbhcokg simpleliealgebrasoverfieldsofpositivecharacteristicstructuretheory |