Jordan algebras over icosahedral cut-and-project quasicrystals

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-09-11 DOI:10.1016/j.geomphys.2025.105645

Daniele Corradetti , David Chester , Raymond Aschheim , Klee Irwin

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引用次数: 0

Abstract

In this paper we present a general setting for aperiodic Jordan algebras arising from icosahedral quasicrystals that are obtainable as model sets of a cut-and-project scheme with a convex acceptance window. In these hypotheses, we show the existence of an aperiodic Jordan algebra structure whose generators are in one-to-one correspondence with elements of the quasicrystal. Moreover, if the acceptance window enjoys a non-crystallographic symmetry arising from

H_{2}, H_{3}

H_{4}

then the resulting Jordan algebra enjoys the same

H_{2}, H_{3}

H_{4}

symmetry. Finally, we present as special cases some examples of Jordan algebras over a Fibonacci-chain quasicrystal, a Penrose tiling, and the Elser-Sloane quasicrystal.

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二十面体切割投影准晶体上的约当代数

本文给出了由二十面体准晶体产生的非周期约当代数的一般设置，这些代数可作为具有凸接受窗口的切割投影格式的模型集。在这些假设中，我们证明了一个非周期约当代数结构的存在性，其产生子与准晶体的元素是一一对应的。此外，如果接收窗口具有由H2、H3或H4引起的非晶体对称性，则所得的约当代数具有相同的H2、H3或H4对称性。最后，我们给出了斐波那契链准晶体、Penrose平铺和Elser-Sloane准晶体上Jordan代数的一些特例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity