Abstract
ABSTRACT An infinite rank affine Lie algebra 𝔤 is a Kac-Moody algebra associated with an infinite affine matrix. For each nonnegative integer l, 𝔤 contains a subalgebra 𝔤l which is a classical finite dimensional simple Lie algebra, 𝔤 0 ⊂ 𝔤 1 ⊂ ± b ··· and 𝔤 is the inductive limit of the set {𝔤i, i = 0, 1,…} of these subalgebras. In the present article, we will determine all automorphisms of 𝔤 leaving 𝔤ni invariant for each {ni} in a set {ni}, where the set {ni, i = 1, 2,…} is any given nonnegative integer sequence with n1 < n2 < ···. These automorphisms are generalizations of automorphisms of classical finite dimensional Lie algebras.
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