Extensions and Well's type exact sequence of skew braces

Abstract

In this article, we give a description of the split exact sequences of left skew braces. We define a free action of the second cohomology group of a left skew brace $H$ by $Ann(I)$ on $Ext_{\alpha}(H, I)$ and show that this action becomes transitive if $I$ is a trivial skew brace. We also generalize the Well's type exact sequence for extensions by the trivial skew brace.