Schur covers of skew braces

TL;DR

This paper develops the theory of Schur covers for finite skew braces, establishing their existence, properties, and relation to projective representations, with explicit examples and structural insights.

Contribution

It introduces the concept of Schur covers for finite skew braces, proves their existence, and explores their properties and applications in representation theory.

Findings

Existence of at least one Schur cover for finite skew braces

Schur covers are isoclinic to each other

Schur covers have a lifting property for projective representations

Abstract

We develop the theory of Schur covers of finite skew braces. We prove the existence of at least one Schur cover. We also compute several examples. We prove that different Schur covers are isoclinic. Finally, we prove that Schur covers have the lifting property concerning projective representations of skew braces.