Download E-books Simple Lie Algebras over Fields of Positive CharacteristicIII. Completion of the Classification GEM 57 (de Gruyter Expositions in Mathematics) PDF

The matter of classifying the finite-dimensional easy Lie algebras over fields of attribute p > zero is a long-standing one. paintings in this query over the last forty five years has been directed by way of the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed box of attribute p > five a finite-dimensional constrained basic Lie algebra is classical or of Cartan variety. This conjecture was once proved for p > 7 through Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the overall case of no longer unavoidably constrained Lie algebras and p > 7 was once introduced in 1991 through Strade and Wilson and finally proved via Strade in 1998. the ultimate Block-Wilson-Strade-Premet type Theorem is a landmark results of glossy arithmetic and will be formulated as follows: each finite-dimensional uncomplicated Lie algebra over an algebraically closed box of attribute p > three is of classical, Cartan, or Melikian kind. within the three-volume booklet, the writer is assembling the facts of the category Theorem with causes and references. The aim is a state of the art account at the constitution and category conception of Lie algebras over fields of optimistic attribute resulting in the vanguard of present learn during this box. this is often the final of 3 volumes. during this monograph the facts of the class Theorem provided within the first quantity is concluded. It collects all of the very important effects at the subject which might be discovered merely in scattered clinical literatur thus far.

Show description

Read Online or Download Simple Lie Algebras over Fields of Positive CharacteristicIII. Completion of the Classification GEM 57 (de Gruyter Expositions in Mathematics) PDF

Best Abstract books

Basic Real and Abstract Analysis

This 1968 variation covers the next themes: Orientation; units and areas; sequences and sequence; degree and integration; degree idea; continuity; derivatives; and stieltjes integrals.

Braid Groups (Graduate Texts in Mathematics)

During this well-written presentation, stimulated by way of various examples and difficulties, the authors introduce the fundamental idea of braid teams, highlighting a number of definitions that exhibit their equivalence; this is often through a therapy of the connection among braids, knots and hyperlinks. very important effects then deal with the linearity and orderability of the topic.

Algebra V: Homological Algebra (Encyclopaedia of Mathematical Sciences)

This quantity of the Encyclopaedia offers a contemporary method of homological algebra, that is in line with the systematic use of the terminology and ideas of derived different types and derived functors. The e-book includes purposes of homological algebra to the idea of sheaves on topological areas, to Hodge conception, and to the speculation of sheaves on topological areas, to Hodge conception, and to the idea of modules over jewelry of algebraic differential operators (algebraic D-modules).

Class Field Theory (Universitext)

This publication offers an available creation to type box concept. It takes a standard technique, yet in a manner that is cleanser and extra streamlined than such a lot different books in this subject. The e-book has been class-tested, and the writer has integrated routines.

Extra info for Simple Lie Algebras over Fields of Positive CharacteristicIII. Completion of the Classification GEM 57 (de Gruyter Expositions in Mathematics)

Show sample text content

Rated 4.27 of 5 – based on 49 votes