  The transformation properties of a Kalb-Ramond field are those of a gauge
potential. However, it is not clear what is the group structure to which these
transformations are associated. In this paper, we complete a program started in
previous articles in order to clarify this question. Using the spectral
theorem, we improve and generalize previous approaches and find the possible
group structures underneath the 2-form gauge potential as extensions of Lie
groups, when its representations are assumed to act into any tensor (or spinor)
space with inner product.
  We also obtain a fundamental representation where a two-form field turns out
to be a connection on a flat Euclidean basis manifold, with a corresponding
canonical curvature. However, we show that these objects are not associated to
space-time tensors and, in particular, that a standard Yang-Mills action is not
relativistically invariant, except (as expected) in the Abelian case. This is
our main result, from the physical point of view.
