Structure Theory.

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...

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Bibliographic Details
Main Author: Strade, Helmut
Format: eBook
Language:English
Published: Berlin/Boston : De Gruyter, 2017.
Edition:2nd ed.
Series:De Gruyter expositions in mathematics.
Subjects:
Lie algebras.
Lie algebras
Online Access:Click for online access
Table of Contents:
  • Introduction ; 1. Toral subalgebras in p-envelopes ; 1.1 p-envelopes ; 1.2 The absolute toral rank ; 1.3 Extended roots ; 1.4 Absolute toral ranks of parametrized families ; 1.5 Toral switching ; 2. Lie algebras of special derivations ; 2.1 Divided power mappings.
  • 2.2 Subalgebras defined by flags 2.3 Transitive embeddings of Lie algebras ; 2.4 Automorphisms and derivations ; 2.5 Filtrations and gradations ; 2.6 Minimal embeddings of filtered and associated graded Lie algebras ; 2.7 Miscellaneous ; 2.8 A universal embedding.
  • 2.9 The constructions can be made basis free 3. Derivation simple algebras and modules ; 3.1 Frobenius extensions ; 3.2 Induced modules ; 3.3 Block's theorems ; 3.4 Derivation semisimple associative algebras ; 3.5 Weisfeiler's theorems ; 3.6 Conjugacy classes of tori.
  • 4. Simple Lie algebras 4.1 Classical Lie algebras ; 4.2 Lie algebras of Cartan type ; 4.3 Melikian algebras ; 4.4 Simple Lie algebras in characteristic 3 ; 5. Recognition theorems ; 5.1 Cohomology groups ; 5.2 From local to global Lie algebras ; 5.3 Representations.
  • 5.4 Generating Melikian algebras 5.5 TheWeak Recognition Theorem ; 5.6 The Recognition Theorem ; 5.7 Wilson's Theorem ; 6. The isomorphism problem ; 6.1 A first attack ; 6.2 The compatibility property ; 6.3 Special algebras ; 6.4 Orbits of Hamiltonian forms.

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