Real and imaginary roots

  • Victor G. Kac
Part of the Progress in Mathematics book series (PM, volume 44)


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.


Real Root Simple Root Finite Type Cartan Matrix Imaginary Root 
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Bibliographical notes and comments

  1. Kac, V. G. [1968 B] Simple irreducible graded Lie algebras of finite growth, English translation: Math. USSRIzvestija 2 (1968), 1271–1311.Google Scholar
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  4. Kac, V. G., Peterson, D. H. [1983 A] Infinite dimensional Lie algebras, theta functions and modular forms, Advances in Math., 50 (1983).Google Scholar
  5. Frenkel, I. B. [ 1983 ] Representations of Kac-Moody algebras and dual resonance models IAS, preprint.Google Scholar
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  10. Lepowsky, J., Moody, R. V. [1979] Hypèrbolic Lie algebras and quasi-regular cusps on Hilbert modular surfaces, Math. Ann. 245 (1979), 63–88.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • Victor G. Kac
    • 1
  1. 1.Mathematics DepartmentMassachusetts Institute of TechnologyCambridgeUSA

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