Classifying the Absolute Toral Rank Two Case (Hardcover, 2nd ed.)

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 algebras 1-sections Sandwich elements and rigid tori Towards graded algebras The toral rank 2 case

General

Imprint:	De Gruyter
Country of origin:	Germany
Series:	De Gruyter Expositions in Mathematics
Release date:	April 2017
First published:	2017
Authors:	Helmut Strade
Dimensions:	240 x 170mm (L x W)
Format:	Hardcover - Cloth over boards
Pages:	394
Edition:	2nd ed.
ISBN-13:	978-3-11-051676-0
Categories:	Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory
LSN:	3-11-051676-4
Barcode:	9783110516760

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