The group structure of non-Abelian NS-NS transformations

We study the transformations of the worldvolume fields of a system of multiple coinciding D-branes under gauge transformations of the supergravity Kalb-Ramond field. We find that the pure gauge part of these NS-NS transformations can be written as a U(N) symmetry of the underlying Yang-Mills group, but that in general the full NS-NS variations get mixed up non-trivially with the U( N). We compute the commutation relations and the Jacobi identities of the bigger group formed by the NS-NS and U( N) transformations.