Generalized non-associative structures on the 7-sphere

Details Generalized non-associative structures on the 7-sphere Generalized non-associative structures on the 7-sphere

2011-09-05

arxiv.org/abs/1109.0859v1

J.Phys.:Conf.Ser. 343, 012026, 2012

Physics

Mathematical Physics

36 pages, JPConf style

Scientific paper

10.1088/1742-6596/343/1/012026

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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