Affine extensions of non-crystallographic Coxeter groups induced by projection

DOI10.1063/1.4820441zbMath1291.20037arXiv1110.5228OpenAlexW3105739404WikidataQ56003525 ScholiaQ56003525MaRDI QIDQ5409674

Pierre-Philippe Dechant, Céline Boehm, Reidun Twarock

Publication date: 14 April 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.5228

zbMATH Keywords

affine extensionsCoxeter-Dynkin diagramsnon-crystallographic Coxeter groupscrystallographic latticesaffine extended root systems

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Reflection groups, reflection geometries (51F15) Root systems (17B22)

Related Items (9)

Clifford algebra is the natural framework for root systems and Coxeter groups. Group theory: Coxeter, conformal and modular groups ⋮ The \(E_8\) geometry from a Clifford perspective ⋮ Reduction of orbits of finite Coxeter groups of non-crystallographic type ⋮ Clifford algebra unveils a surprising geometric significance of quaternionic root systems of Coxeter groups ⋮ From the Trinity ( A ₃ , B ₃ , H ₃ ) to an ADE correspondence ⋮ Viruses and fullerenes – symmetry as a common thread? ⋮ Group-theoretical analysis of aperiodic tilings from projections of higher-dimensional latticesB_n ⋮ Orbits of crystallographic embedding of non-crystallographic groups and applications to virology ⋮ A Clifford algebraic framework for Coxeter group theoretic computations.

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