  We construct an explicit equivalence between a category of complexes over the
exterior algebra, which we call HT-complexes, and the stable category of vector
bundles on the corresponding projective space, and establish a relation between
HT-complexes and the Tate resolutions over the exterior algebra, which had been
described by D. Eisenbud, G. Floystad, F.O. Schreyer in math.AG/0104203. The
correspondence between HT-complexes and stable classes of vector bundles
essentially translates into more fancy terms former results of Trautmann on
representing Koszul complexes, which, in turn, were influenced by ideas of
Horrocks. However, the relation between the Tate resolutions over the exterior
algebra and HT-complexes might be new, although, perhaps, not a surprise to
experts.
