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October 2, 2025Open Access

The nilpotent graph of a finite0-dimensional Lie algebra

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The nilpotent graph characterizes nilpotent elements in finite-dimensional Lie algebras, revealing structural properties.
When the characteristic of the field is zero, nilpotent elements and the hypercenter coincide.
The nilpotentizer's behavior under direct sums allows decomposition of the nilpotent graph's components effectively.
Computations for the algebra reveal that the nilpotent graph can be decomposed into multiple components, each regular in structure.

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This paper investigates properties of nilpotent graphs in finite-dimensional Lie algebras, focusing on nilpotentizer and hypercenter relationships.

Towers et al. (2025) studied this question.

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This paper investigates properties of nilpotent graphs in finite-dimensional Lie algebras, focusing on nilpotentizer and hypercenter relationships.