Abstract
In this paper, the strongly ad‐nilpotent elements of the Lie algebra of upper triangular complex matrices are studied. We prove that all the nilpotent matrices in are strongly ad‐nilpotent if and only if n ≤ 6. Additionally, we prove that all the elements exp(ad x), x strongly ad‐nilpotent generate the inner automorphism group Int t(n, ℂ).
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