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Journal of Lie Theory 30 (2020), No. 4, 1027--1046
Copyright Heldermann Verlag 2020

Derivations of the Lie Algebra of Strictly Block Upper Triangular Matrices

Prakash Ghimire
Dept. of Mathematics and Physical Sciences, Louisiana State University, Alexandria, U.S.A.

Huajun Huang
Dept. of Mathematics and Statistics, Auburn University, Auburn, U.S.A.


\newcommand\Der{\operatorname{Der}} \newcommand\N{\mathcal N} Let $\N$ be the Lie algebra of all $n \times n$ strictly block upper triangular matrices over a field $\mathbb{F}$. Let $\Der(\N)$ be Lie algebra of all derivations of $\N$. In this paper, we describe the elements and the structure of $\Der(\N)$. We also determine the dimensions of component subalgebras of $\Der(\N)$.

Keywords: Derivation, nilpotent Lie algebra, strictly block upper triangular matrix.

MSC: 17B40, 16W25, 15B99, 17B05.

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