On groups of $I$-type and involutive Yang-Baxter groups

Abstract

We suggest a cohomological framework to describe groups of $I$-type and involutive Yang-Baxter groups. These groups are key in the study of involutive non-degenerate set-theoretic solutions of the quantum Yang-Baxter equation. Our main tool is a lifting criterion for 1-cocycles, established here in a general non-abelian setting.