Structure Theory.
- 2nd ed.
- 1 online resource (550 pages)
- De Gruyter Expositions in Mathematics Series ; v.38 .
- De Gruyter Expositions in Mathematics Series .
Intro -- 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 -- 6.5 Hamiltonian algebras -- 6.6 Contact algebras -- 6.7 Melikian algebras -- 7. Structure of simple Lie algebras -- 7.1 Derivations -- 7.2 Restrictedness -- 7.3 Automorphisms -- 7.4 Gradings -- 7.5 Tori -- 7.6 W(1 -- n) -- 8. Pairings of induced modules -- 8.1 Cartan prolongation -- 8.2 Module pairings -- 8.3 Trigonalizability -- 9. Toral rank 1 Lie algebras -- 9.1 Solvable maximal subalgebras -- 9.2 Cartan subalgebras of toral rank 1 -- Notation -- Bibliography -- Index.