Author | Samelson, Hans. author |
---|---|
Title | Notes on Lie Algebras [electronic resource] / by Hans Samelson |
Imprint | New York, NY : Springer New York, 1990 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-9014-5 |
Descript | XII, 162 p. 3 illus. online resource |
1 Generalities -- 1.1 Basic definitions, examples -- 1.2 Structure constants -- 1.3 Relations with Lie groups -- 1.4 Elementary algebraic concepts -- 1.5 Representations; the Killing form -- 1.6 Solvable and nilpotent -- 1.7 Engelโs theorem -- 1.8 Lieโs theorem -- 1.9 Cartanโs first criterion -- 1.10 Cartanโs second criterion -- 1.11 Representations of A1 -- 1.12 Complete reduction for A1 -- 2 Structure Theory -- 2.1 Cartan subalgebra -- 2.2 Roots -- 2.3 Roots for semisimple g -- 2.4 Strings -- 2.5 Cartan integers -- 2.6 Root systems, Weyl group -- 2.7 Root systems of rank two -- 2.8 Weyl-Chevalley normal form, first stage -- 2.9 Weyl-Chevalley normal form -- 2.10 Compact form -- 2.11 Properties of root systems -- 2.12 Fundamental systems -- 2.13 Classification of fundamental systems -- 2.14 The simple Lie algebras -- 2.15 Automorphisms -- 3 Representations -- 3.1 The Cartan-Stiefel diagram -- 3.2 Weights and weight vectors -- 3.3 Uniqueness and existence -- 3.4 Complete reduction -- 3.5 Cartan semigroup; representation ring -- 3.6 The simple Lie algebras -- 3.7 The Weyl character formula -- 3.8 Some consequences of the character formula -- 3.9 Examples -- 3.10 The character ring -- 3.11 Orthogonal and symplectic representations -- References -- Symbol Index