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

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 gen...

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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2022-01, Vol.2022 (1)
Main Author: Hu, Zhiguang
Format: Article
Language:English
Subjects:
Algebra
Automorphisms
Decomposition
Eigenvalues
Lie groups
Mathematics
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Summary: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.
ISSN:2314-4629
2314-4785
DOI:10.1155/2022/3484381