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
Kac, V. G. [ 1968 A] Graded Lie algebras and symmetric spaces, Funkt. analys. i ego prilozh. 2 (1968), No. 2, 93–94
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© 1983 Springer Science+Business Media New York
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Kac, V.G. (1983). Affine Lie algebras: the realization (case k=2 or 3). Application to the classification of finite order automorphisms. In: Infinite Dimensional Lie Algebras. Progress in Mathematics, vol 44. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-1382-4_8
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DOI: https://doi.org/10.1007/978-1-4757-1382-4_8
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4757-1384-8
Online ISBN: 978-1-4757-1382-4
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