  As an application of Roberts' cohomology (net cohomology), we prove the
completeness of the DHR sectors of the local observables of the model in the
title, detailed in [8]. This result is achieved via the triviality of the net
1-cohomology, with values in the local fields, enhancing the Roberts' methods
to the case of anyonic Weyl nets, not satisfying the split property. We take
advantage of using different causal index sets for the nets involved. The
presence of anyonic commutation relations is treated introducing the notion of
nets graded by a generic group, and the related properties of graded locality
and graded duality. As a further result, we obtain the description of twisted
and untwisted sectors of the model as two symmetric subcategories of a
W*-braided category, whose objects are the same as the dual category of the
compact Abelian group of the gauge symmetry. The work also furnish some hints
for the analysis of the sector structure of generic models on different
spacetimes.
