Advances in Applied Clifford Algebras

, Volume 22, Issue 3, pp 757–769 | Cite as

On the Ternary Approach to Clifford Structures and Ising Lattices

Open Access


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.

Mathematics Subject Classification (2010)

Primary 82C44 Secondary 82D25 81R05 15A66 


Clifford algebra crystal lattice Ising lattice Jordan algebra octonions quaternions sedenions 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.


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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Institute of PhysicsUniversity of ŁódźŁódźPoland
  2. 2.Institute of MathematicsPolish Academy of Sciences, Łódź BranchŁódźPoland
  3. 3.Department of Computer and System Analysis, College of Humanities and SciencesNihon UniversitySetagaya-ku, TokyoJapan
  4. 4.Department of Relativity PhysicsUniversity of Warmia and MazuryOlsztynPoland

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