# Universal central extensions of Hom-Lie antialgebras

## TL;DR

This paper develops a theory of universal central extensions for Hom-Lie antialgebras, establishing conditions for their existence and characterizing their kernels via homology groups.

## Contribution

It introduces the concept of universal central extensions in Hom-Lie antialgebras and proves their existence is equivalent to the algebra being perfect.

## Key findings

- A Hom-Lie antialgebra admits a universal central extension if and only if it is perfect.
- The kernel of the universal central extension equals the second homology group with trivial coefficients.
- The paper provides foundational results linking homology and extension theory in Hom-Lie antialgebras.

## Abstract

We develop a theory of universal central extensions for Hom-Lie antialgebra. It is proved that a Hom-Lie antialgebra admits a universal central extension if and only if it is perfect. Moreover, we show that the kernel of the universal central extension is equal to the second homology group with trivial coefficients.