Yang-Baxter deformations beyond coset spaces(a slick way to do TsT)

Yang-Baxter string sigma-models provide a systematic way to deform coset geometries, such as $Ad{S}_p\times S^p$, while retaining the $\sigma$-model integrability. It has been shown that the Yang-Baxter deformation in target space is simply an open-closed string map that can be defined for any geometry, not just coset spaces. Given a geometry with an isometry group and a bivector that is assumed to be a linear combination of antisymmetric products of Killing vectors, we show the equations of motion of (generalized) supergravity reduce to the Classical Yang-Baxter Equation associated with the isometry group, proving the statement made in https://arxiv.org/abs/1710.06784. These results bring us closer to the proof of the "YB solution generating technique" for (generalized) supergravity advertised in https://arxiv.org/abs/1710.06784 and in particular provide an economical way to perform TsT transformations.