On one dimensional Leibniz central extensions of a naturally graded filiform Lie algebra

TL;DR

This paper classifies Leibniz central extensions of a naturally graded filiform Lie algebra, providing explicit classifications in low dimensions and invariant functions for parametric families.

Contribution

It offers a detailed classification of Leibniz central extensions for a specific class of Lie algebras, including explicit isomorphism classes and invariant functions.

Findings

Classified low-dimensional central extensions.

Identified invariant functions for parametric families.

Provided a basis simplifying the multiplication table.

Abstract

This paper deals with the classification of Leibniz central extensions of a naturally graded filiform Lie algebra. We choose a basis with respect to that the table of multiplication has a simple form. In low dimensional cases isomorphism classes of the central extensions are given. In parametric family orbits cases invariant functions (orbit functions) are provided.