Affine Lie algebras: the realization (case k=1)

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


In this chapter we describe in detail a “concrete” construction of all “nontwisted” affine Lie algebras. It turns out that such an algebra g can be realized entirely in terms of an “underlying” simple finite dimensional Lie algebra ġ. Namely, its derived algebra [g, g] is the universal central extension (the center being 1-dimensional) of the Lie algebra of polynomial maps from ℂX into ġ. In fact, the “Fourier transform” of the latter algebra appears in the quantum field theory, and is called a current algebra.


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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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