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Yang-Baxter string sigma-models provide a systematic way to deform cosetgeometries, such as $AdS_p \times S^p$, while retaining the $\sigma$-modelintegrability. It has been shown that the Yang-Baxter deformation in targetspace 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 bivectorthat is assumed to be a linear combination of antisymmetric products of Killingvectors, we show the equations of motion of (generalized) supergravity reduceto the Classical Yang-Baxter Equation associated with the isometry group,proving the statement made in [1]. These results bring us closer to the proofof the "YB solution generating technique" for (generalized) supergravityadvertised in [1] and in particular provide an economical way to perform TsTtransformations.

Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)