Article

Advances in Applied Clifford Algebras

, Volume 22, Issue 3, pp 757-769

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

On the Ternary Approach to Clifford Structures and Ising Lattices

  • J. ŁawrynowiczAffiliated withInstitute of Physics, University of ŁódźInstitute of Mathematics, Polish Academy of Sciences, Łódź Branch Email author 
  • , O. SuzukiAffiliated withDepartment of Computer and System Analysis, College of Humanities and Sciences, Nihon University
  • , A. NiemczynowiczAffiliated withDepartment of Relativity Physics, University of Warmia and Mazury

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 82C44 Secondary 82D25 81R05 15A66

Keywords

Clifford algebra crystal lattice Ising lattice Jordan algebra octonions quaternions sedenions