Skew braces from Rota–Baxter operators: a cohomological characterisation and some examples

Rota–Baxter operators for groups were recently introduced by Guo, Lang, and Sheng. Bardakov Gubarev showed that with each operator, one can associate a skew brace. Skew braces on group G be characterised in terms of certain gamma functions from to its automorphism $${{\,\mathrm{Aut}\,}}(G)$$ are defined functional equation. For the obtained corresponding take values inner $${{\,\mathrm{Inn}\,}}(G)$$ G. In this paper, we give characterisation G, , come vanishing element suitable second cohomology group. Exploiting characterisation, able exhibit examples whose group, but cannot operator. operators, show how get latter former, exploiting knowledge central extension splits.