Strongly Ad-Nilpotent Elements of the Lie Algebra of Upper Triangular Matrices

Zhiguang Hu and Naihuan Jing

Journal of Mathematics, 2022, vol. 2022, 1-5

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

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:3484381

DOI: 10.1155/2022/3484381

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