Аннотация:In this paper, we study representations of G_n^3-like groups. The group G_n^3 itself appeared in works of the third named author on non-Reidemeister knot (and braid) theory. This group is closely related to dynamical systems of points and their invariants. Representations of G_n^3-like groups are useful both for the study of those groups themselves, and constructing invariants of knots and braids based on the G_n^3-like group structure.