Yang-Baxter structure of the extended space

Abstract: We construct an analogue of Yang--Baxter deformations defined by a single Killing vector, that is a solution generating transformation in Einstein--Maxwell dilaton theory. We show that these are nothing but a coordinate transformation in a parent theory related to EMd theory by KK reduction. Similarly (almost-abelian) bi-vector Yang--Baxter deformations are coordinate transformations in the doubled space.