Tensor Products are Projective Geometries Original Research Article

Given a finite-dimensional vector spaceV, we construct a family of projective geometries whose flats are certain subspaces ofV, and show that there is a one-to-one correspondence between this family of projective geometries and the set of equivalence classes of tensor decompositions ofV. This provides a practical method for finding a tensor decomposition of a finite-dimensionalKG-module or proving that no nontrivial tensor decomposition exists.