I in generalized supergravity

We showed in previous work that for homogeneous Yang-Baxter (YB) deformations of AdS(5)xS(5) the open string metric and coupling and as a result the closed string density e-2 Phi root g remain undeformed. In this work, in addition to extending these results to the deformation associated with the modified CYBE or eta-deformation, we identify the Page forms as the open string counterpart for RR fields and demonstrate case by case that the non-zero Page forms remain invariant under YB deformations. We give a physical meaning to the Killing vector I of generalized supergravity and show for all YB deformations: (1) I appears as a current for the center of mass motion on the worldvolume of a D-brane probing the background, (2) I is equal to the divergence of the noncommutativity parameter, (3) I exhibits "holographic" behavior where the radial component of I vanishes at the AdS boundary and (4) in pure spinor formalism I is related to a certain state in the BRST cohomology.