Division Algebras, Clifford Algebras, Periodicity


The dimensions 2, 8 and 24 play significant roles in lattice theory. In Clifford algebra theory there are well-known periodicities of the first two of these dimensions. Using novel representations of the purely Euclidean Clifford algebras over all four of the division algebras, \({\mathbf{R}}\), \({\mathbf{C}}\), \({\mathbf{H}}\), and \({\mathbf{O}}\), a door is opened to a Clifford algebra periodicity of order 24 as well.

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Dixon, G. Division Algebras, Clifford Algebras, Periodicity. Adv. Appl. Clifford Algebras 28, 13 (2018). https://doi.org/10.1007/s00006-018-0820-8

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