Academic > Mathematics > Download, free read

Lectures on Lie Groups and Lie Algebras by Roger W. Carter download in iPad, ePub, pdf

Universal envelopping algebras Levi'sFor many examples

Universal envelopping algebras, Levi's theorem, Serre's theorem, Kac-Moody Lie algebra, The Kostant's form of the envelopping algebra and A beginning of a proof of the Chevalley's theorem. For many examples, the complete description of the geometry and its basic invariants is worked out in detail. Several applications are discussed throughout the text. Lie groups, Lie algebra associated to a group, Correspondence between groups and algebras, classification of connected compact Lie groups, theory of Cartan Weyl. It is shown how to use infinite dimensional representations to derive the Weyl character formula.