Simple Lie algebras over fields of positive characteristic . II Classifying the absolute toral rank two case [[electronic resource] /] / by Helmut Strade

• Record Nr.: UNINA9910818400603321
• Autore: Strade Helmut <1942->
• Pubbl/distr/stampa: Berlin ; ; New York, : Walter de Gruyter, 2009
• ISBN: 1-282-34530-3; 9786612345302; 3-11-916446-1; 3-11-020305-7
• Descrizione fisica: 1 online resource (391 p.)
• Collana: De Gruyter expositions in mathematics ; ; 42
• Disciplina: 512/.55
• Soggetti: Lie algebras; Algebra
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliography and index.
• Nota di contenuto: Frontmatter -- Contents -- Introduction -- Chapter 10. Tori in Hamiltonian and Melikian algebras -- Chapter 11. 1-sections -- Chapter 12. Sandwich elements and rigid tori -- Chapter 13. Towards graded algebras -- Chapter 14. The toral rank 2 case -- Chapter 15. Supplements to Volume 1 -- Backmatter
• Sommario/riassunto: 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 during the last 45 years 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 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 leading to the forefront of current research in this field. This is the second part of the three-volume book about the classification of the simple Lie algebras over algebraically closed fields of characteristics › 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 Aleksei. I. Kostrikin and Alexander A. Premet and the investigation of absolute toral rank 2 simple Lie algebras over algebraically closed fields of characteristics › 3 is given.