The aim of this chapter is to give the definition of Kac—Moody Lie algebras and establish their most basic properties, which we will need subsequently in the book. The basic reference for this chapter as well as Chapter 2 (barring the discussion of the Shapovalov form as in Subsections 2.3.1-2.3.8) is Kac’s book [Kac-90] which exhaustively treats the algebraic theory of Kac—Moody Lie algebras and their representations.
KeywordsBilinear Form Weyl Group Coxeter Group Casimir Operator Simple Reflection
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