On the Ternary Approach to Clifford Structures and Ising Lattices

被引：0
|
作者：
J. Ławrynowicz
O. Suzuki
A. Niemczynowicz
机构：
[1] University of Łódź,Institute of Physics
[2] Polish Academy of Sciences,Institute of Mathematics
[3] Łódź Branch,Department of Computer and System Analysis, College of Humanities and Sciences
[4] Nihon University,Department of Relativity Physics
[5] University of Warmia and Mazury,undefined
来源：
Advances in Applied Clifford Algebras | 2012年 / 22卷
关键词：
Primary 82C44; Secondary 82D25; 81R05; 15A66; Clifford algebra; crystal lattice; Ising lattice; Jordan algebra; octonions; quaternions; sedenions;
D O I：
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中图分类号：
学科分类号：
摘要：
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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页码：757 / 769
页数：12
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