Generalized non-associative structures on the 7-sphere

Autor(es)

da Rocha, Roldao ; Traesel, Marcio A. ; IOP

• Tipo de documento: Artigo Científico
• Fonte: WAKE CONFERENCE 2021; v. 343, p. 36-pg., 2012-01-01.

Resumo

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 Cl-0,Cl-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]. (AU)

• Processo FAPESP: 11/08710-1 - 7th International Conference on Quantum Theory and Symmetries
• Beneficiário: Roldão da Rocha
• Modalidade de apoio: Auxílio à Pesquisa - Reunião - Exterior