Tensor Products are Projective Geometries

✍ Scribed by C.R Leedham-Green; E.A O'Brien

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 197 KB
• Volume: 189
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1996.6881

✦ Synopsis

Given a finite-dimensional vector space V, we construct a family of projective geometries whose flats are certain subspaces of V, 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 of V. This provides a practical method for finding a tensor decomposition of a finite-dimensional KG-module or proving that no nontrivial tensor decomposition exists.