Abstract
We continue to modify and simplify the Ising-Onsager-Zhang procedure for analyzing simple orthorhombic Ising lattices by considering some fractal structures in connection with Jordan and Clifford algebras and by following Jordan-von Neumann-Wigner (JNW) approach. We concentrate on duality of complete and perfect JNW-systems, in particular ternary systems, analyze algebras of complete JNW-systems, and prove that in the case of a composition algebra we have a self-dual perfect JNW-system related to quaternion or octonion algebras. In this context, we are interested in the product table of the sedenion algebra.
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In memory of Professor Jaime Keller
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Ławrynowicz, J., Suzuki, O. & Niemczynowicz, A. On the Ternary Approach to Clifford Structures and Ising Lattices. Adv. Appl. Clifford Algebras 22, 757–769 (2012). https://doi.org/10.1007/s00006-012-0360-6
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DOI: https://doi.org/10.1007/s00006-012-0360-6