Tri-vector deformations in d=11 supergravity

We construct a d = 11 supergravity analogue of the open-closed string map in the context of SL(5) Exceptional Field Theory (ExFT). The deformation parameter tri-vector Omega generalizes the non-commutativity bi-vector parameter Theta of the open string. When applied to solutions in d = 11, this map provides an economical way of performing TsT deformations, and may be used to recover d = 10 Yang-Baxter deformations after dimensional reduction. We present a generalization of the Classical Yang-Baxter Equation (CYBE) for rank 3 objects, which emerges from d = 11 supergravity and the SL(5) ExFT. This equation is shown to reduce to the d = 10 CYBE upon dimensional reduction.