Simple Lie Algebras over Fields of Positive Characteristic. / Volume 2, : Classifying the Absolute Toral Rank Two Case / / Helmut Strade.

• Superior document: Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package
• VerfasserIn: Strade, Helmut,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2017]; ©2017
• Year of Publication: 2017
• Edition: 2nd ed.
• Language: English
• Series: De Gruyter Expositions in Mathematics , 42
• Physical Description: 1 online resource (VIII, 386 p.)

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 classification of the simple Lie algebras over algebraically closed fields 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 algebras1-sectionsSandwich elements and rigid toriTowards graded algebrasThe toral rank 2 case

Table of Contents

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 -- Notation -- Bibliography -- Index