Advances in Applied Clifford Algebras

, Volume 22, Issue 3, pp 757–769

On the Ternary Approach to Clifford Structures and Ising Lattices

Open AccessArticle

DOI: 10.1007/s00006-012-0360-6

Cite this article as:
Ławrynowicz, J., Suzuki, O. & Niemczynowicz, A. Adv. Appl. Clifford Algebras (2012) 22: 757. doi:10.1007/s00006-012-0360-6

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.

Mathematics Subject Classification (2010)

Primary 82C44Secondary 82D2581R0515A66

Keywords

Clifford algebracrystal latticeIsing latticeJordan algebraoctonionsquaternionssedenions
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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