2004/02/28 by Bertfried Fauser · 1 voice
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #Coproduct #Eigenvalues and eigenvectors #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Morphism #Singular value #Singular value decomposition #Tensor algebra #Tensor product #math-ph #math.MP #msc:15A18 #msc:15A66 #msc:16W30
paper · pdf · doi:10.1007/s10773-006-9111-6
published as Int. J. Theor. Phys. Vol 45, No 9, 2006: 1731-1755 · 17 pages, three eps-figures
arxiv created 2004/02/28 · arxiv published 2004/02/28 · arxiv updated 2004/02/28 · openalex publication_date 2006/08/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Products and coproducts may be recognized as morphisms in a monoidal tensor category of vector spaces. To gain invariant data of these morphisms, we can use singular value decomposition which attaches singular values, ie generalized eigenvalues, to these maps. We show, for the case of Grassmann and Clifford products, that twist maps significantly alter these data reducing degeneracies. Since non group like coproducts give rise to non classical behavior of the algebra of functions, ie make them noncommutative, we hope to be able to learn more about such geometries. Remarkably the coproduct for positive singular values of eigenvectors in A yields directly corresponding eigenvectors in A⊗ A.