Lie Algebras of Finite and Affine Type

Liealgebrashavemanyvariedapplications,bothinmathematicsandmathematicalphysics.Thisbookprovidesathoroughbutrelaxedmathematicaltreatmentofthesubject,includingboththeCartan-Killing-WeyltheoryoffinitedimensionalsimplealgebrasandthemoremoderntheoryofKac-Moodyalgebras.Proofsaregivenindetailandtheonlyprerequisiteisasoundknowledgeoflinearalgebra.ThefirsthalfofthebookdealswithclassificationofthefinitedimensionalsimpleLiealgebrasandoftheirfinitedimensionalirreduciblerepresentations.ThesecondhalfintroducesthetheoryofKac-Moodyalgebras,concentratingparticularlyonthoseofaffinetype.AbriefaccountofBorcherdsalgebrasisalsoincluded.AnAppendixgivesasummaryofthebasicpropertiesofeachLiealgebraoffiniteandaffinetype.