Jordan algebras over icosahedral cut-and-project quasicrystals

2023/03/21 by Daniele Corradetti, David Chester, Corradetti, Daniele +5 · 1 voice
Engineering · Materials Science · Mathematics · #Quasicrystal Structures and Properties #graph theory and CDMA systems #math.RA

paper · pdf · doi:10.48550/arxiv.2303.12219

openalex publication_date 2023/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 hypothesis, 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 H2, H3 or H4 then the resulting Jordan algebra enjoys the same H2, H3 or H4 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.

Discussions

• In particular the set you get is *not* dense in the plane: iopscience.iop.org/article/10.1... These folks claim quasiaddition obeys axioms that let you construct a Jordan algebra from a quasicrystal: [bsky, 7 points, 2 comments]

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