Real and imaginary roots
In this chapter we give an explicit description of the root system ∆ of a Kac-Moody algebra g(A). Our main instrument is the notion of an imaginary root, which has no counterpart in the finite-dimensional theory.
KeywordsReal Root Simple Root Finite Type Cartan Matrix Imaginary Root
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Bibliographical notes and comments
- Kac, V. G. [1968 B] Simple irreducible graded Lie algebras of finite growth, English translation: Math. USSRIzvestija 2 (1968), 1271–1311.Google Scholar
- Moody, R. V.  Root systems of hyperbolic type, Adv. in Math. 33 (1979), 144–160.Google Scholar
- Kac, V. G., Peterson, D. H. [1983 A] Infinite dimensional Lie algebras, theta functions and modular forms, Advances in Math., 50 (1983).Google Scholar
- Frenkel, I. B. [ 1983 ] Representations of Kac-Moody algebras and dual resonance models IAS, preprint.Google Scholar