Novel Kac-Moody-type affine extensions of non-crystallographic Coxeter groups

Dechant, Pierre-Philippe; Boehm, Celine; Twarock, Reidun

doi:10.1088/1751-8113/45/28/285202

Novel Kac-Moody-type affine extensions of non-crystallographic Coxeter groups

Dechant, Pierre-Philippe; Boehm, Celine; Twarock, Reidun

Authors

Pierre-Philippe Dechant

Celine Boehm

Reidun Twarock

Abstract

Motivated by recent results in mathematical virology, we present novel asymmetric -integer-valued affine extensions of the non-crystallographic Coxeter groups H2, H3 and H4 derived in a Kac–Moody-type formalism. In particular, we show that the affine reflection planes which extend the Coxeter group H3 generate (twist) translations along two-, three- and five-fold axes of icosahedral symmetry, and we classify these translations in terms of the Fibonacci recursion relation applied to different start values. We thus provide an explanation of previous results concerning affine extensions of icosahedral symmetry in a Coxeter group context, and extend this analysis to the case of the non-crystallographic Coxeter groups H2 and H4. These results will enable new applications of group theory in physics (quasicrystals), biology (viruses) and chemistry (fullerenes).

Citation

Dechant, P., Boehm, C., & Twarock, R. (2012). Novel Kac-Moody-type affine extensions of non-crystallographic Coxeter groups. Journal of Physics A: Mathematical and Theoretical, 45(28), Article 285202. https://doi.org/10.1088/1751-8113/45/28/285202

Journal Article Type	Article
Publication Date	Jul 20, 2012
Deposit Date	Jan 20, 2014
Publicly Available Date	Feb 12, 2014
Journal	Journal of Physics A: Mathematical and Theoretical
Print ISSN	1751-8113
Electronic ISSN	1751-8121
Publisher	IOP Publishing
Peer Reviewed	Peer Reviewed
Volume	45
Issue	28
Article Number	285202
DOI	https://doi.org/10.1088/1751-8113/45/28/285202