Tri-vector deformations on compact isometries

Classical Yang–Baxter equation governing bi-vector deformations of 10d supergravity is known to have no solutions along non-abelian compact isometries. By providing explicit examples we show that this is in contrast to generalized Yang–Baxter equation governing tri-vector deformations of 11d supergravity. We present deformations of the AdS$${}_7\times \mathbb {S}^4$$ and flat backgrounds with isometries generated by Killing vectors of a sphere. Isometries of the AdS space-time are preserved by such deformations