Abstract
An invertible linear map φ on a Lie algebra L is called a triple automorphism of it if φ([x, [y, z]]) = [φ(x), [φ(y), φ(z)]] for ∀ x, y, z ∈ L. Let g be a finite-dimensional simple Lie algebra of rank l defined over an algebraically closed field F of characteristic zero, p an arbitrary parabolic subalgebra of g. It is shown in this paper that an invertible linear map φ on p is a triple automorphism if and only if either φ itself is an automorphism of p or it is the composition of an automorphism of p and an extremal map of order 2.
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Supported by “the National Natural Science Foundation of China” (Grant No. 11171314) and “the Fundamental Research Funds for the Central Universities” (2010LKSX05).
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Wang, D., Yu, X. Triple automorphisms of simple Lie algebras. Czech Math J 61, 1007–1016 (2011). https://doi.org/10.1007/s10587-011-0043-9
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DOI: https://doi.org/10.1007/s10587-011-0043-9