Uniconnected solutions to the Yang–Baxter equation arising from self-maps of groups

Abstract

Abstract Set-theoretic solutions to the Yang–Baxter equation can be classified by their universal coverings and their fundamental groupoids. Extending previous results, universal coverings of irreducible involutive solutions are classified in the degenerate case. These solutions are described in terms of a group with a distinguished self-map. The classification in the nondegenerate case is simplified and compared with the description in the degenerate case.