  Using group theoretical methods we show for both the triangular and square
lattices that in the continuum limit the antiferromagnetic order parameter
lives on SO3 without respect of the initial lattice. For the antiferromagnetic
chain we recover the Haldane decomposition. This order parameter interacts with
a local gauge field rather than with a global one as implicitly suggested in
the literature which in our approach appears in a rather natural manner. In
fact this merely corresponds to a novel extension of the spin group by a local
gauge field. This analysis based on the real division algebras applies to low
dimensional lattices.
