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Affine Lie algebras: the realization (case k=2 or 3). Application to the classification of finite order automorphisms

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

Abstract

Here we describe a realization of the remaining, “twisted” affine Lie algebras. This turns out to be closely related to the Lie algebra of equivariant polynomial maps from it ℂX to a simple finite-dimensional Lie algebra with the action of a finite cyclic group. As a side result of this construction we deduce a nice description of the finite order automorphisms of a simple finite-dimensional Lie algebra, and, in particular, the classification of symmetric spaces.

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Bibliographical notes and comments

  1. Kac, V. G. [ 1968 A] Graded Lie algebras and symmetric spaces, Funkt. analys. i ego prilozh. 2 (1968), No. 2, 93–94Google Scholar
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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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