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Format: 1 online resource

ISBN: 9783110197945

Series Statement: De Gruyter Expositions in Mathematics ; 38

Note: Frontmatter -- , Contents -- , Introduction -- , Chapter 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 -- , Chapter 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 -- , Chapter 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 -- , Chapter 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 -- , Chapter 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 The Weak Recognition Theorem -- , 5.6 The Recognition Theorem -- , 5.7 Wilson's Theorem -- , Chapter 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 -- , Chapter 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;ṉ) -- , Chapter 8: Pairings of induced modules -- , 8.1 Cartan prolongation -- , 8.2 Module pairings -- , 8.3 Trigonalizability -- , Chapter 9: Toral rank 1 Lie algebras -- , 9.1 Solvable maximal subalgebras -- , 9.2 Cartan subalgebras of toral rank 1 -- , Notation -- , Bibliography -- , Index

Additional Edition: ISBN 978-3-11-014211-2

Language: English

DOI: 10.1515/9783110197945

URL: https://doi.org/10.1515/9783110197945