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 Extα(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.