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 $Ex{t}_{\alpha }(H,I)$ 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.

comments are welcome. arXiv admin note: text overlap with arXiv:2102.12235

Cited by in corpus (3)

• Extensions and automorphisms of Rota-Baxter groups
• Hopf formulae for homology of skew braces
• Cohomology and Extensions of Relative Rota-Baxter groups