2011/09/05 by Roldão da Rocha, Roldao da Rocha, M. A. Traesel +1 · 14 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic and Geometric Analysis #Associative property #Bundle #Clifford algebra #Clifford analysis #Clifford bundle #Context (archaeology) #Frame bundle #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematics #Normal bundle #Pure mathematics #Vector bundle #hep-th #math-ph #math.MP #math.QA #msc:15A66
paper · pdf · doi:10.1088/1742-6596/343/1/012026
published in Journal of Physics Conference Series 343, 012026 (IOP Publishing) · 36 pages, JPConf style
arxiv created 2011/09/05 · openalex publication_date 2012/02/08 · arxiv updated 2012/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we provide a more general class of non-associative products using the exterior and Clifford bundles on the 7-sphere S 7 . Some additional properties encompass the previous formalisms presented in [1, 2] in the Clifford algebra context, and wider classes of non-associative structures on S 7 are investigated, evinced by the directional non-associative products and the mixed composition of generalized non-associative products between Clifford algebra multivectors. These non-associative products are further generalized by considering the non-associative shear of arbitrary Clifford bundle ℓ 0,7 elements into octonions. We assert new properties inherited from the non-associative structure introduced in the whole Clifford bundle on S 7 , which naturally induce involutions on the Clifford bundle and provide immediate generalizations concerning well-established formal results in, e.g., [3, 4, 5, 6, 7] and potential applications in physics as pioneered by, e. g., [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14].