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