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arXiv · 1109.0859

Generalized non-associative structures on the 7-sphere

Roldao da Rocha·M. A. Traesel
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Abstract

In this paper we provide a more general class of non-associative products using the exterior and Clifford bundles on the 7-sphere. Some additional properties encompass previous formalisms in the Clifford algebra context, and wider classes of non-associative structures on the 7-sphere 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(0,7) elements into octonions. We assert new properties inherited from the non-associative structure introduced in the whole Clifford bundle on S7, which naturally induce involutions on the Clifford bundle and provide immediate generalizations concerning well-established formal results and potential applications in physics.

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Roldao da Rocha, M. A. Traesel. 2011-09-05. Generalized non-associative structures on the 7-sphere. https://doi.org/10.1088/1742-6596/343/1/012026

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