TENSOR-PRODUCTS ARE PROJECTIVE GEOMETRIES

Given a finite-dimensional vector space V, we construct a family of pr ojective geometries whose flats are certain subspaces of V, and show t hat there is a one-to-one correspondence between this family of projec tive geometries and the set of equivalence classes of tensor decomposi tions of V. This provides a practical method for finding a tensor deco mposition of a finite-dimensional KG-module or proving that no nontriv ial tensor decomposition exists. (C) 1997 Academic Press.