  The purpose of the paper is to prove an analogous correspondence for the
above prehomogeneous vector space (1)-(3). For case (1) the correspondence is
bijective. However, it turns out that the correspondence is not bijective for
cases (2), (3). We describe the fiber structures of this correspondence in
subsection 2-4. In section 1 we briefly review basic properties of the
non-abelian Galois cohomology set and its relation to the orbit space G_k \
V_k^ss. In subsection 2-4 we consider the prehomogeneous vector spaces (1)-(3)
respectively.
