Extensions and Well’s type exact sequence of skew braces

Abstract

In this paper, we describe the split exact sequences of skew left braces. We define a free action of the second cohomology group of a skew left brace [Formula: see text] by [Formula: see text] on [Formula: see text] and show that this action becomes transitive if [Formula: see text] is a trivial skew brace. We also generalize the Well’s type exact sequence for extensions by the trivial skew brace.